czwartek, 6 października 2016

Density of the Universe

Contents
1.  The density of the Universe in the first (Newtonian) approach. Short introductory resume.  
     Flatness of the geometry of the Universe. Calculation of density of the Universe. Density dependence on 
     time.    
2. Critical density. Calculation of the critical density using
     simplified  Weinberg’s method. Calculation on the basis of

     Friedmann equation.


1. The density of the Universe in the first (Newtonian) approach                                         Those who will say to themselves: "Here it goes, the continuation of that naïve cosmology" surely won’t read it. The previous article they also left unread with a sense of superiority of an "initiate". And I go on. I envy those who are so sure of everything.
Short introductory resume                                                                                                         In the preceding article we have concluded that he mass of the Universe (meaning the Contractual Mass of Universe (CMU)) gradually increases, moreover it increases in coordination with the increase in its size. This makes me (not just me) ask the questions: What is its density? Does it remain constant? Of course not, because the volume increases faster than the mass, in proportion to the third power of the parameter defining the dimensions and it does not matter what is the actual topology of the Universe. However, so as to estimate (density), we should perform the appropriate calculations. For this purpose, we assume (tentatively) that the Universe is a sphere with a radius equal to the Schwarzschild radius. This can be done provided that the geometry of the Universe is flat*. This is, of course, an oversimplification, but let's not quarrel about the values of small deviations. It does not preclude the main goal. Is the geometry of the Universe really flat? According to the concept of this work, the flatness of space is an inherent feature of the Universe as a whole. The rationale for such a view is the assertion that "the building stuff of space is the relative motion of material objects." Motivational basis for this approach is also embodied in one of the (already stated) conclusions based on the cosmological principle, indicating that the resultant intensity of the global gravitational field is equal to zero. So this is not about the expansion of curved (by gravity) space - as it is thought in relation to the fact that today's cosmology is based on the field equations of general theory of relativity (GTR). It is interesting that with this, according to today's views, the expansion has not been caused by gravity, since it "only attracts". [And pressures? They were introduced to justify the possibility of repulsion by those unaware of the possibility of dual gravity. According to the hypothesis of inflation, at some point there was great pressure, which was equated with a negative gravity. In general, pressure is the second, besides attraction, element in the description of the Universe on the basis of GTR. For this reason, there are three options for the development of expansion (Friedmann’s models).] The Explosion itself together with inflation is a matter of quantum field theory (some mismatches, vacuum energy, the Higgs field, the inflation field bubble, etc.), in which gravity is neglected, even ignored. But after inflation, development of the object proceeded according to GTR equations and the theory of gravity. It ought to be admitted that its field equations contain all options of the beginnings, without going into the processes at the level of the structure of matter (...).
  While I persistently claim that the cause of expansion is in fact gravity. Dual Gravity. So there was no baton transfer as in a relay. This is clearly indicated in articles 4-7.          
     Currently, as I have noted above, the causes of the Explosion are attributed to the quantum microstructure of being, the vacuum energy recognized as an indisputable fact, and its fluctuation all of a sudden, which was to lead directly to the Big Bang. It was then that time allegedly began its existence (And what was before?). “First (right after the beginning) the events were caused by fluctuation of some inflation field, existing through the concept of inflation, then gravity started its work (when this something became flesh), which essence is solely attraction, although the Universe (exclusively) was fitted with the repulsion chip (pressure generated by the "dust"), and then, relatively recently, Einstein’s mistake was reactivated, that is the cosmological constant, and it was associates with the "invention" of dark energy..." Muddle? The less we understand nature the more complex it becomes.  
And exactly where this vacuum energy comes from? The hypothesis of its existence derives from calculations within the framework of the quantum field theory. So it is huge, given the scale of our perception. I am full of admiration for scholars who have come to this without in any way considering gravity (the one in sub-dimensions, gravity at the Planck scale). By the way, at great cost of time and work by the greatest minds. I had it a lot easier, thanks to them.             
Considering the elementary gravity (articles 5-8) we discover another world – let’s just remember the (absolute) maximum force of attraction between the two plankons, enormous even in astronomical scale. Let’s recall still greater (64X), maximum repulsive force of gravity – it is exactly this force which caused that event which we call the Big Bang. I think that the reader can already guess everything. Is it really about a mysterious vacuum energy, detectable only in the equations of quantum field theory (and not in experience); about nothingness masking potential enormity? The enormity of what? It borders on mysticism. Rather not gravity, I think, which is not recognized by the quantum mechanics. This (masking) is facilitated by the fact that in the atomic scale and in the scale of particles, as well as in our macroscopic scale, gravity is extremely weak. But we (and only we here) already know that the cause of this weakness is the almost total compensation of gravitational forces in the subatomic scale. Thanks to what? Thanks to dual gravity, thanks to the existence of a niche, gravitational potential energy - a place where particles can be created. So there are particles, atoms, there is the whole of our world. After all, if somewhere deep there was no repulsion, everything would disappear in an infinite black abyss. Could the matter at all come into existence? Nobody cares. "But we have the Pauli exclusion principle." And where does it come from? The job is performed by equations.  
Flatness of the geometry of the Universe.  
 And in the scale of our senses? At present the subject is based on the Friedmann equation (including the cosmological constant and dark energy) and on current knowledge of the microworld (quantum mechanics), while the unfortunate, " flatness of the Universe" is the result of observation. Is something wrong? Also the mathematical superstructure pretending to the role of the base, even absolute, and argumentation based on it plays here its prominent (if not fundamental) role. Is that how it should be? Rather not. The effect should not precede the cause. Nature does not need to adapt to the connotations resulting from equations devised to the extent of human's limited capabilities.  
 Flatness means that the density parameter (ratio of the average density of the Universe to the critical density) Ω = 1. As the most reliable calculations (of course based on the Friedmann equation - not necessarily correct) indicate, if in the first second from the beginning of the expansion this parameter was only slightly greater than unity, the Universe would have collapsed long time ago. If it were only slightly less than unity, the atoms could not be created (as a result of too rapid dissipation of matter). We just wouldn’t exist. And yet maybe even as much as 15 billion years have passed from the start of expansion. Robert Dicke in one of his lectures presented it in a very demonstrative way: „When the age of the universe was equal to one second, the value of the parameter Ω could not exceed the range of 1±0.00000000000000001", for the Universe to have current features of the structure of matter and the dynamics of development**. The flatness problem. Strange balancing of the Universe on the rope of a hair thickness. Is that the reason for the adoption of the anthropic principle? Personally, I reject this principle, seeing it even as a kind of mysticism (in a materialistic frame). Reason: below. By the way, earlier, already in the initial part of the previous article I stated that due to the inherent flatness of the space of the Universe, "criticality" is the only option. In this situation we can’t talk about criticality due to its semantics, and the density parameter loses its usefulness as only equal to one. Here we’ve got the base for a new cosmology.
   At present that is not seen this way. It is accepted that nowadays the density parameter is indeed (let's say "approximately") equal to unity, but perhaps in the future its value will be different, that’s why the symbol Ω is often accompanied by index zero. In addition, in accordance with today's modelling, its value results from a variety of factors independent of each other, which may mean that the unit value of omega is not all that obvious, it may be even accidental. The mind boggles at the observation made by Robert Dicke. According to the model which I present, this "randomness" is not possible (as randomness). According to the model presented here Ω does not change. The flatness of space is an objective feature of nature, and not an improbable state aimed at ensuring our existence. A little more and we’ll come to think that this is because everything that surrounds us is, for each of us individually, only an impression, as it was stated hundreds of years ago by certain Berkeley. Thus, the Universe was not created purposely for our existence, and its description based on basic and universal laws of nature is simpler, without any a hint of purposefulness... 
Calculation of the density of the Universe                                                                                    ...In any case, concerning the flatness of the Universe consensus omnium predominates, because this is indicated by observations. So let’s calculate the density of the Universe assuming (in this case perfectly digestible) simplification that the Universe is a spherical object. Thus: 
Here R –Schwarzschild (gravitational) radius: R = 2GM÷c^2. In view of the assumed flatness the Universe can be treated as a sphere of radius R. So we get:  
As you can see, judging from this formula, the density of the Universe (as well as the density of an object enclosed within the gravitational radius, called the black hole) is inversely proportional to the square of its mass, which, as we know, is increasing. I will refer to this formula time and again.
Density dependence on time 
So it is interesting how this density relates to time. For this purpose we use the postulated in the previous article equality of gravitational and Hubble radiuses. The Hubble law should be also taken into account.
However this non-linearity can be described differently, and thus avoid inconsistencies brought about by this hypothesis. Suffice to assume that the initial dimensions of the Universe were not zero. Then the non-linearity of increase in size is natural in view of the target speed c. The model corresponding to this thesis is described in the third part of the article entitled: "The first moments of the Big Bang", though quite a lot I blurted out earlier. The nonlinear expansion of my breeding, not based on "inflationary" assumptions I called: Urela (Ultra-Relativistic acceleration). In those very early times there wasn’t either the electromagnetic interaction, and so there was no limitation concerning the speed of expansion - as one might think.
So first we transform the formula for the Schwarzschild radius:                                             
and apply the Hubble’s law in relations to the horizon: c = HR. Thus we get: 

Here τ is the age of the Universe. Finally by joining formulas (1) and (2) we obtain the formula for the average density of the Universe:                
We see that the average density of the Universe depends explicitly of the value of constant H, and is proportional to its square (or inversely proportional to the square of the age of the Universe). [For the record, so defined age of the Universe is sometimes called the Hubble’s time. It is believed that to determine the (real) age of the Universe, the gravitational slowing down of the expansion (predicted by the Friedmann equation) must be taken into consideration as well as its acceleration due to dark energy. I see no justification for such an approach. I think that the "idealization" in the context of our discussion is in fact closer to the truth as it is freed from the imperfections of human investigative insight.] Let’s note also that in the last formula there is no constant c. So, according to this dependence the speed of light bears no relation to changes of density of the Universe. This does not mean that this speed is really constant against global time.  
     It is noteworthy that we deduced this formula starting from adopted in the previous article postulate of equality of gravitational and Hubble radiuses. We will get this formula following also a different, more agreed path. It is not a novelty. Currently this postulate surprises, in any case those to whom I present my thoughts. [In general, beforehand I invite them to supply themselves with a bottle of mineral water.] As it will (surprisingly) turns out further on, this postulate leads to the result concurrent with the calculation forecasting the development of the Universe in accordance with the critical model, constituting, as we know, one of the three options resulting from the Friedmann equation. Therefore, this "other way" of mine is not "so" meaningless in spite of the fact that it does not fully comply with the Friedman’s version, even in relation to "criticality". The point is that despite the (modelled here) flatness, the Universe, in relation to assumed periodicity of its physical and spatial characteristics, will not expand asymptotically toward infinity (as expected by equation Friedmann equation for the critical model). Yes, periodicity, not only postulated but simply justified on the basis of various criteria, to the extent that it "cannot be otherwise". Is it only my subjective conviction? Of course not. Many wiser than me are convinced about the periodicity of Nature. The problems which they encountered are essentially of doctrinal character, for example, "What to do with the increase of entropy?”. The question of entropy I will also address in due time. 
     The conviction of cyclicality can draw support from the ancient philosophical thought (not forgetting the intellectual heritage of the peoples of America before the arrival of the barbarians from Christian Europe. Now there are already other barbarians. Those have already invaded Europe.
They haven’t yet managed to learn humanity. They need for it hundreds of years and millions of victims of self-destruction under the imperative of hatred for someone completely different... Well, Homo Sapiens. How strange that they send their countrymen to virgins, instead of, for this godly purpose, blowing their own brains out. No, first they have to play some martyr’s jihad. This does not disturb political correctness, what matter is that they want to annihilate those whom Europe did not quite manage in its time. That was rather common in antiquity. Are humans really growing? The (negative) measure of growth is the potential of hatred. Ahead of us, humans, still a long way to go.
     An alternative to cyclicality in the form of a semi-infinity (because Everything had its beginning and stretches to infinity), though supported by the authorities of the church, does not seem serious. It simply gives an impression of an ontological botch. The Creator was not a bungler! Today, this strange alternative is accepted as if in the nature of things, and moreover, with "deep understanding".
     And (here) we have flatness of space, combined with cyclicality. Along with this, in a concept that I present, we have the development of the Universe: determined, occurring in one direction only. This is about the only possible process in the sense that there cannot be any alternative of various options (as it’s the case with three models in the Friedmann equation). Nature is one, and its description should therefore be unambiguous. And this is not about the content of my findings, not about "this particular model", but about the uniqueness of objective being. It’s about the idea of uniqueness. There is simply no more than one possibility. This means that even this particular, presented here model of the Universe is more credible with respect to the objectively existing nature than the traditional one. The Universe is simply not "this or that" (depending on the results of measurement). The theory not providing for a univocal development is only (and at most) a tentative model. I think that’s how we should treat Friedmann equation.
   Also, consideration of matters in the category of probability is here (I think) pointless. The Universe as such is, I emphasize again, determined. It cannot be described by some wave function. The Universe is simply a kind of an absolute and human perception does not have anything to do with. Epistemological superstructure should have no influence on the objective facts we learn and will learn in the future. And the anthropic principle? For me it’s a kind of oddity, which "emotional" premises I do not share. Excessive anthropocentrism? (Subconscious) recurrence to hierarchizing by Thomas Aquinas and geocentricism in the new edition? Relapses? Well, cyclicality does not bypass us either. This principle is most probably the result of the frustration of science at the crossroads. I encourage you to read Lee Smolin’s book***.

Purposefulness, a reversal of cause and effect. All of these arguments in support of the anthropic principle do not amount to any evidence. They lead astray. In 1600 Giordano Bruno was burned at the stake for having had the audacity to claim that there are other worlds where there is life, perhaps similar to our own. Since that time more than 400 years have passed, and mankind has not learned much despite technological and scientific achievements (in fact of only a handful of people). As a mass we are mentally far from these achievements. The evolution of life on Earth has been going on for more than 3 billion years. There was enough time. Unless someone thinks that the whole world began 5,776 years ago. In this case any questioning is unquestionably impossible. 

If the anthropic principle is a consequence of today's paradigms, it is a sign that we should discard some of them. When examining Nature and studying its objective laws one should be guided by simplicity and discard anthropocentrism.
     Another thing that research as such, observations, along with a variety of interpretations, the whole cognitive dynamics which has its main source in curiosity, is something extremely interesting and worthy of separate studies. It is for the pious. The search for truth of nature (and other objective truths), is also one of the essential elements of what should constitute the basis for humanistic thought, even if the search dissociates itself from the "anthropo-activism". How many declared humanists have that outright paranoid hatred (of course in relation to people)... This transpires in many Parlour (Salon in Polish) scraps and comments (Salon24.pl), not to mention the less intelligent portals. Among the real investigators of Nature (including human nature) hate is a rather rare phenomenon.
     Returning to equation (3) let’s note also that there is no mass in it, even though density is the invariant mass. In fact, this was to be expected given that the mass is an extensive value. Does this apply to the mass of the entire Universe? Here I would be careful.
This means unambiguity of being, you might say: absoluteness. In any case, the Creator knew what he was doing. Perhaps this way should lead the path to understanding Nature, even if the nature of the Creator is semantically undetermined (usually everything is limited to pagan idolatry, including kissing pictures and teaching of hatred in accordance with the priority of love of one’s neighbour).
What is the average density of the Universe? Anyone can calculate it for him/herself.
2. Critical density
Above we derived the density of the Universe based on the postulated equality of Hubble and gravitational radiuses of the Universe. Additionally I relied on the assumption of flatness of the geometry of the Universe, which I supported with perfectly acceptable rational premises. The flatness is also indicated by observation [even if it is (conceptually) surprising to some]. As for the flatness there is consensus omnium despite the fact that in my humble opinion it is an inherent, and not an "approximate" feature of the Universe.

Calculation of the critical density using simplified Weinberg’s method.
"Flatness", according to today's views, means that the Universe develops in accordance with the critical model, one of the three predicted by the Friedmann equation. It is therefore of critical density. [Almost, but we do not know which way. I omit here inflation, which eliminated this problem by smoothing everything to fit the order.] Let's calculate it using two different approaches. First one is actually a description of the method used by Steven Weinberg in his famous book “The First Three Minutes”, a description designed for lay persons. 
We choose at random a galaxy. Its mass is equal to m, and the radial velocity relative to us (in the cosmological sense) is equal to v. Its distance from us equals r. We constitute the origin of the coordinate system and, of course, the centre of the Universe. According to the cosmological principle each observer will tell you the same regardless of the galaxy it inhabits. Our chosen galaxy is located on the surface of a fictitious sphere of radius r, including certain number of galaxies, including ours (along with interstellar matter), which mass is M*. As a base we will use the Newton’s law of universal gravitation. It is known that the remaining Universe, apart for the chosen galaxy, bears no gravitational impact on the outcome of our deliberations. Just like a layer of any thickness above a person measuring his/her weight, and located at a certain depth below the surface. There, that person’s weight is determined solely by the mass of this part of the Globe, which lies below. In the centre the weight of each body is equal to zero. This can be proven by calculation. A more general description of this rule is expressed by Gauss' law, which is also true with respect to the electrostatic field. The potential energy of the galaxy (more precisely, the energy of its interaction with the rest located below) is equal to:
Its radial velocity, according to the Hubble’s law: v = Hr, so its kinetic energy:    
Thus, the total energy: 
After substituting in place of the mass:   
which can be done since we assume that space is flat, we get:
(We remember that, according to the cosmological principle, the local density, although of cosmological importance, is everywhere the same.)
The galaxy we have chosen can be on the very horizon, because we have not limited the distance at which it is located. Then the total mass "under" it:  M* → M is the mass of the whole Universe. The above equations remain, obviously, in force. Let us discuss the formula (4). We can immediately see that there are three possibilities. When E > 0, which means that the numerical value of the potential energy is less than the value of kinetic energy, and gravity is too weak to stop expansion – the opened model. When E<0, we have the reversed situation, gravity is strong enough to stop the expansion and cause in the aftermath of the collapse of the Universe. Of course, we are talking here about the closed model. When E = 0, the Universe develops according to the critical model. This is the case of our interest. From the formula (4), we obtain:   
Here: ρc – critical density of the Universe. As it comes out, following completely different path we have come to formula (3). We received the equation for the critical density identical to the formula for the density of the Universe based on the postulate of the equality of gravitational and Hubble radiuses. I think there is something in it, even if it's surprising. Here, however, it is about the critical density, and this is one of three possibilities, actually the improbable one, since it is the point border (see the previous chapter). However, in connection with a fairly strong indication of the flatness of the Universe, researchers’ attention has focused precisely on this option. The problem, however, lies in the fact that the observationally detected mass (actually the density parameter derived from the mass of the visible, and even the dark matter), is too small to ensure criticality.
In view of the above the search for additional mass (to achieve the critical density) is quite understandable. Or maybe the search for this additional mass is unnecessary? Is it certain that the density parameter is the proper indicator or that its measurement is correct? The question is justified not only for those who share my view that the GTR (say in the Friedmann version) is not the appropriate tool for cosmological determinations. And if we do not use the GTR and are not interested in the critical density, then the search for density parameter is beside the point. Heresy chases heresy. 
The observational determination of the average density is not an easy thing. Not all matter is visible, and it is not always is possible to determine it. An example of such efforts is the measurement of the amount of deuterium, which was created at the beginning of nucleosynthesis, in the early phase of BB, probably only then. The results, however, are far from expectations.
In the concept proposed in this work the problem of the value of density parameter does not exist, and "adding" mass equivalent to dark energy (apparently up to 70% of the mass of the Universe) is probably a big misunderstanding, it is simply a fiction, multiplication of entities beyond need. Perhaps today's concept of Ω measurement is at fault (and apart, also the treatment of this parameter as binding and mandatory). But this lack of mass had to be filled in some way. Hence the uncritical enthusiasm for the idea of dark energy. All en-masse herded this way and many were amply rewarded with PhDs and professorships. Even Mr. Nobel was seduced. [Wait, repulsion (dark energy) points to the negative mass, therefore these 70% should have been subtract (not added). We would get not 100% but 40% ... And here, as if out of spite, the space is flat.]
   My insolent approach is consistent with the previously expressed opinion that the Universe available to observation comprises its totality. Obviously this is not consistent with the currently applicable rules and presumptions (not to say prejudices). So as to appease the more incensed readers (fundamentalism is now in vogue) I admit that for the time being this opinion is not the final judgement banishing today's views. If someone was to be banished, then (as it can be seen in each case) it would have to be the writer of this work, despite the fact that he is basing it on rather rational assumptions, in any case no less rational than those which serve as basis for opposed views. It so happens that he was already exiled many years ago and for the completely different reasons****. But never mind.
     Coming back to the interrupted thought we should add that if in spite of everything, there is something beyond the horizon (as it is thought by the majority of those interested), the consideration of this would be something purely speculative, not much adding to the final vision due to its unprovability.
Here is the numerical value of the critical density corresponding to our assumed value of constant H = 20: 
It is of course today’s value. Let’s compare this value with the density determined on the basis of estimated in the previous article mass of the Universe and its corresponding Schwarzschild radius (here expressed in light years). Here is the calculation of density:                  
The results of these calculations are very close to each other. This probably testifies in favor of the concept presented in this article. [Anyone who read it all carefully knows that it is all clear of any "sly adjustments". I did not have to do that. And even if, then we still have a unique convergence given the same numbers, which we had at our disposal - huge. The probability of coincidence is virtually nil. Incidentally, the "sly adjustment" is used widely nowadays. Take the hypothesis of inflation. In that case "slyness" breaks all records.]

Calculation of critical density based on Friedman equation. 
Let us make the next step. Here's Friedman equation:              
where ȧ  the scale factor of the Universe (dot at the top means its derivative with respect to time), k – a constant value in time and in space, describes the geometry of the Universe, type of its curvature. 
k > 0 means spherical curvature of the closed Universe, k < 0 – hyperbolic curvature of the open Universe, and k = 0 – flat space in which the Universe evolves according to the critical model. Here we should add that the value c^2 (square of the speed of light) in general, especially in the professional writings, is ignored due to the assumption that it is equal to unity. This is justified not only by practical consideration (simplified calculation). But let’s not stray from the subject.
The scale factor (a) is a function of time and is directly related to the pace of expansion. If within certain time the factor, for example, triples, it means that the dimensions of the Universe have also tripled. This expansion, however, is not an "explosion of a grenade". It is the expansion of space which contains matter (according to today's understanding). This results in continued increase of distances between galaxies (in the cosmological scale), although it is not about their relative movement in the Newtonian sense. Can we therefore say that the movement is cosmological scale is not a kinematic quality in the Newtonian sense? This would result in a very convenient conclusion that relative "speed" of objects may exceed, even significantly, the speed of light in a vacuum. It would suffice that they were adequately distant from each other, far enough that it would not be possible to have coordination between them in less than the age of the Universe. This apparently happened in time of the so-called inflation, and the existence of these appropriately remote objects is its consequence.
So the whole expansion is a "personal" matter of  space-time, and galaxies remain, in fact, at rest relative to each other (not taking into account their insignificant (?) local movements), despite the resulting from it expansion and mutual distancing. [Would that mean that the actual movement is purely local, and cosmology is something else?] What is this constant distance between them (if not taking into account the Friedmann expansion)? – one could ask. Very interesting question, particularly in view of the adopted by some, even a priori, thesis that Everything started from (let say: almost) a point singularity. So are we talking here about the arbitrariness and activism of space against inertia and passivity of matter? Why not? What about De Sitter’s model? Yes, but the magnitude of curvature depends directly on the total mass. Also, on the mass of the smallest bodies, even the elementary particles... Well, yes, it is, after all, about the mutually moving coordinates.           
According to the concept presented in this work, which is, among other things, to serve as a checking test (by its alternativeness) maybe even for the sake of today's beliefs, it is after all about the actual movement, though in a closed (not Newtonian-infinite) space. Closed by the fact that it is contained within specific topological formation, which characteristics are indicated by  the features of the evolution of the Universe, suggested in the text and in different contexts. This formation makes the Universe a periodically variable creation.
Let us return to Friedman equation. Let’s consider the first part of its right side, and actually its dimension: 1/s^2 (the square of the inverse unit of time). The same dimension applies of course to the left side, which features the scale factor a. The dimension of the left side indicates that the scale factor has the dimension of length. So we have here the square of ratio of speed to distance. The meaning of distance is here, however, somewhat different than usually, because it is the magnitude associated with the expansion of space. There can be demonstrated the consistency of the thesis that the amount constituting the left side of the equation is equal to the square of the Hubble factor. [Let’s note that it is enough to change the letters in Hubble’s law, and represented the speed as a derivative of distance (r) with respect to time.] Therefore it seems to be perfectly valid to observe that constant H itself defines the rate of expansion. [The term "the rate of expansion" was introduced (actually derived) already in the second article.] Its decrease with time would mean the gradual reduction of this rate, which would correspond to slowing the movement of a body thrown upwards (and to diminishing curvature of space). My approach is different. For the record, the consistent application of the cosmological principle leads to the conclusion that global cosmological gravitational field intensity is equal to zero. So there is no question of delay (or acceleration). Thus, the speed at which the Universe expands is determined by the "expansion rate", that is by the upper bound of relative speeds - c, which, according to cosmological principle, is invariant. But let’s go back to our narrative. So we get:  
I noticed it already in the second article. Thus we can formulate the Friedman equation in a slightly modified form:
Using it we can calculate critical density. In this case the curvature (k) is equal to zero. Therefore:
Again, we get a familiar equation. As you can see, the postulated equality of gravitational and Hubble radiuses leads to a formula identical with that derived on the basis of the general theory of relativity. Thus this new path which I have proposed is consistent with the method based on this theory. This is well worth noting. Therefore the postulate of equality of gravitational and Hubble radiuses has some justification, even if it is a surprise. I have already drawn attention to it earlier. Let’s add to this, that this postulate indicates explicitly (and not "one way or the other") the character of expansion, it defines its course as consistent with the view that the space of the Universe is indeed flat, in addition, regardless of time. If so, we made some progress in understanding at least this cosmological issue.

*) Flat geometry is the Euclidean geometry.
**) Information on this subject can be found, among other things, in the book by  
       Alan H. Guth – The inflationary universe.
***) „Kłopoty z fizyką – The trouble with physics” (Prószyński i Ska 2008)
****) Martial law and emigration.








wtorek, 23 sierpnia 2016

And what about the mass of the Universe?

And what about the mass of the Universe?

Contents
Introduction – why mass?
1. Let us estimate the mass of the Universe
2. (Schwarzschild’s) radius of the Universe
3. The mass of the Universe is gradually increasing
4. The mechanism causing the increase in the mass of the
     Universe
5. Reflections and thoughts in the context of estimations about
     the mass of the Universe, or: let’s speculate. The problem of
     saturation
Á propos



Introduction – why mass? 
    One of the conclusions drawn already at the beginning of our cosmological considerations was that the observable Universe, limited by the Hubble horizon, constitutes an absolute Everythingness. To this thesis we shall return repeatedly. It leads to the conclusion that the Universe is quantitatively limited, and even to the conclusion that its substance remains invariant, despite the multitude of changes occurring in it. Apart from it, the adoption of the concept of the Big Bang, most acceptable according to current knowledge, entails the possibility, if not the necessity (not always realized) of accepting just such an approach. After all, if something exploded, it cannot be quantitatively unlimited. This is somehow disregarded. Because it obvious? I'm not sure.
     Already the confirmation of (quantitative) predictions concerning the CMB radiation (see the preceding, that is the seventh article) testifies to the fact that the observable Universe is everythingness, and its current size is determined by the value of H factor and, of course, by the value of invariant c. Due to the fact that the Universe is quantitatively limited, determining its mass makes some sense since it is possible. It wouldn’t make much sense if the Universe was infinite, or its dimensions were unknown and its material content undefinable. Then the density parameter (W) would be the only sensible parameter informing about the material content of the Universe. Today, its mass is not discussed. What does this tell us? I think it tell us that, on the one hand, based on the existing (still in force) views, conclusive determination of full dimensions of the Universe has not been possible [alleged diameter of 92 billion light years is the result of a concept, not of a measurement, the concept that may prove to be a dud – which is about the so-called moving coordinates, in relation to the autonomy of expanding space]; on the other hand, intuitively, perhaps subconsciously, the Universe is still perceived as infinite being (or something like that), despite nearly a century of development of science and today's assertions on the existence of evolution of the Universe and on its changeability. Can something infinite be variable?
    So at present the mass of the Universe is not discussed. Its determination on the basis of observations would be a Sisyphean task. Simply “not everything can be seen.” Apart, the extensiveness* of mass in the face of research necessarily based on observation (without the possibility of conducting experiment), is not a basis for generalizations, for obtaining an overall picture. For this reason, and at this stage rightly, contemporary cosmology uses the intensive* parameter of density. For the record, it is equal to the ratio of the average density of the Universe to its critical density.
   And yet, if we abandon GTR and Friedmann’s equation (worth checking out this possibility, if there is one), then according to the conclusion to which we have come in the previous articles, the use of the concept of critical density is kind of an anachronism, because, as it turns out, it is the sole existing density. In this situation the density parameter Ω = 1, and its usefulness in cosmology decreases to zero – since according to the observations the geometry of the Universe is flat. So what remains? Of course, the mass (what else?), provided that it is really possible to determine the global material content of the Universe. Can it be done? Judging by the discussion conducted so far, this possibility cannot be excluded. So let’s test it out.
   We will therefore take up the problem of mass. In this way we will create the basis for reflections and conclusions that go beyond the standard, falsifiable conclusions, and even anticipating the effects consistent with observation. After all, this is not the Great New Theory, but only checking of specific concepts which would not come about if everything in today's cosmology and astrophysics was ok. But it is not. In relation to "the mass of the Universe", the validity of following this different path I signaled earlier, at it is confirmed by the results of the investigations presented hereunder - maybe quite encouraging... (or) to be rejected categorically and without justification... (?). On this occasion, I strongly urge you to read the articles on the duality of gravity.
And one more thing. Below I will present the reasoning, logical sequence of sentences. This, however, is not a guarantee that all the conclusions are certainties. It is not easy, especially here, to avoid the traps of logic. For this reason, the emerging speculations and hypotheses should be verified. At this stage not everything is closed. Thanks a lot to those who will see the options that I have not taken into account, options that would make the matter even more consistent. And by the way, let’s separate the essential things from the details that further on will prove not to be the most important. What is important are the starting point and the final conclusions, hopefully consistent with the results of our research. 

1. Let us estimate the mass of the Universe
      This is not difficult to do in relation to observable objects. The mass of the Earth is equal to 6·10^24 kg, the mass of the Sun is 333,000 times greater than the mass of the Earth, that is equal to about 2·10^30kg. The mass of an average galaxy is estimated at one hundred billion solar masses, and the total number of galaxies is estimated of the same order of magnitude. Finally, the mass of luminous objects of the Universe can be estimated at 2·10^52kg. The estimation can be also performed in another way. The observational count of galaxies gives their average density. It turns out that on average one galaxy occurs per 1Mps (megaparsec)**. If we assume that the farthest glowing objects are at the distance of 15 billion light years, and assuming that the Universe is a sphere of this radius, and is homogeneous, we get its total mass to be equal to 8.2·10^52kg. This result agrees well with the previous estimate (the same order of magnitude). It can be even “explained” that is greater because it takes into account the mass of matter which doesn’t yet shine with stars, the matter too young for that, located somewhere near the horizon. "Oh, the naivety! It's just a coincidence".
    In our first estimate we took into account only the glowing objects, manifesting their presence by emission of radiation, in particular light. We should also take into account the mass of matter deposited near the horizon (as mentioned above in italics), the matter too young to be able to shine with the light of stars. According to credible research the shining matter of first proto-galaxies appeared about a billion years*** after the Big Bang. This time amounted to 10% of today's age of the Universe. So it can be assumed that the mass of its imperceptible part is quite a significant component of the total mass (approximately 10%).
    Most likely, there is also matter that is not shining - in galaxies and galaxy clusters, and perhaps also in the vast intergalactic regions. Its mass exceeds even the mass of visible matter, up to five times according to today's estimates. The existence of this dark matter can be apparently demonstrated by observational data. Already in the thirties of the last Century there were noted “excessively” fast movements (radial - red-shift) of galaxies in clusters which they form (in Coma Berenices - Fritz Zwicky, in Virgo cluster - Sinclair Smith), and yet there haven’t been noted any disintegration of these clusters. Apparently the total mass of the clusters is much greater. It has been also noted that the rotation of many galaxies is too fast for a large number of stars forming them to be able to exist as stable systems. Conclusion: the actual mass of galaxies is much larger, and this is attributed to the mass of dark matter.

Here it is worth (and appropriate) to mention the attempt to create an alternative to dark matter. In the eighties of last Century, Moti Milgrom, professor at the Weizmann Institute in Israel, developed a theory constituting a modification of the second law of Newton, called MOND (Modified Newtonian Dynamics). Thorough research in the following years did not confirm the validity of this theory. At this point, I suggest a quick return to the content of the first and third articles.
   The existence of dark matter, this time in the intergalactic space, is to be also testified by the intensive motions of galaxies themselves which can’t be explained by anything else, and also by the result of quantitative analysis of the effect of gravitational lensing, observed during the study of distant clusters of galaxies. [The existence of dark matter is indicates by the research carried out in recent years with the help of the Hubble telescope. It turns out that galaxies are arranged in such a way that they form a kind of foam structure. Using the method of gravitational lensing there were explored the areas occupied by galaxies. It is exactly in these areas were the dark matter was found.] To the possibility of the existence of dark matter I pointed out earlier. It can be expected that the dark matter in the intergalactic space, and in the galaxies themselves, is a relic of the early stage of the Explosion, still before the appearance of today’s matter with its weak and strong electric interactions that formed it before the expansion has gained the current characteristics.
   There, in that matter, atoms did not form, there might have remained systems and particles unknown to us, which cannot shine even if concentrated in dense formations, filling and surrounding the visible objects. Perhaps fractals of dark matter had accumulated around themselves other matter that gave rise to the first stars (made of hydrogen, helium and lithium), and then, on a larger scale, galaxies. Perhaps that dark matter contributed to the fragmentation of matter (in the first billion years after the Big Bang), which resulted in the formation of clusters of galaxies, as well as those separating them areas of intergalactic “emptiness”. An example of such an “emptiness” is the Great Attractor, to which, surprisingly, tend numerous galaxies in our area. Our galaxy moves in that direction with a speed of about 600 km/s). Currently, although the existence of dark matter is acknowledged as an unquestionable fact of nature, its structural features, even its material essence, remains a puzzle... An indication as to the nature of this relic matter is presented in the third article. I described this also in an essay dealing with the genesis of galaxies (as for now published in the Polish language):


Here, however, I proceed in a slightly different direction, while considering the Universe in a more complete manner.
     The contribution of neutrinos to the total mass of the Universe is also often pointed out. That’s quite possible. In this context it may be worth looking into the articles on neutrinos (for now only in Polish):
Judging by their content, neutrino warp of space could possibly explain the existence of so-called dark energy, which source remains a mystery to everyone, but to, perhaps, neutrinos (we’ll discuss it further on, although, for other reasons, we won’t pursue this line of reasoning.
     Taking into account the presence of dark matter with its mass five times greater than the mass of luminous matter and based on our initial estimate, we can assume that the mass of the Universe amounts to 10^53kg. This magnitude is generally accepted by many astronomers (even if dealing with the mass of the Universe is in their opinion beside the point). It is of course about an order of magnitude, and not an exact value. Is it the mass of the entire Universe, or only of its visible part? Rather the former.
     For those familiar with the subject that estimate smacks of naivety. Professional approach starts with estimating the value of density parameter which is the ratio of the actual density of the Universe to the critical density... 
This approach enables to skip, in general considerations, the problem of the mass of the Universe, which is a specific value, something that could be philosophically quite awkward. In contrast, the density parameter as the intensive value does not require an answer to the question whether Universe is finite or infinite, it does not involve its “external” parameters. [Exactly. There appear ambiguity, I would say “indeterminancy”, which does not bring us closer to, rather pulls away from the unambiguity of objective natural being, which is the Universe.] It's a good idea, but because of it something (the phenomenological approach) is lost. So we will deal with mass not necessarily as being naive and not only for pedagogical considerations. This approach is justified by the resulting conclusions. Even stronger justification of this approach I gave already in the Introduction, as well as in earlier articles, when discussing the CMB radiation, and in particular when noting congruity of the results of measurements with predictions. Let’s continue.
 ... The determination of density parameter is based on observational data, especially on the evaluation of the content of deuterium in the cosmic space. Based on these data it is estimated that the contribution of visible matter is approx. 5%. It is surprisingly little, as observational data indicate that the density parameter has a value close to (“maybe” equal to) unity (100%). What about the rest? The rest is, in the (current) opinion of scholars: the dark matter (25%) and the equivalent of the above-mentioned so-called dark energy, which, in Einstein's field equations was expressed by the cosmological constant, which was introduced (and rejected) by Einstein and today revived (up to 70%). To tell the truth, these figures do not quite match our conclusion on the mass of the Universe. It should be therefore rejected. But before we do that, let’s calculate...  
It may be worth to stop here for a moment of reflection. Is gravitational energy everything (even if we reject the dark energy)? For there is also the thermodynamic internal energy. The temperature of the Universe is not zero (and it won’t be). It came into being, as we know, during the phase transition at the beginning of BB, as a result of dissipation of part of kinetic energy of the Urela expansion. The magnitude of this energy does not change in spite of its growing dilution during the process of expansion. This factor must be considered when balancing the total energy, which is obviously equivalent to mass. It can be a significant part of the mass of the Universe. This thermal energy makes itself felt at least by luminosity of all matter (in all ranges of the spectrum), and by relict radiation. Maybe that's why in our initial estimate of the mass of luminous objects was so accurate, maybe that's why our estimated mass of the Universe, as we shall see, is the key to something quite new and very promising. Here it is worth recalling the Appendix to the article fifth on the energy contained in the gravitational field.

2. ...(Schwarzschild’s) radius of the Universe
     For the record (and to put it simply), it is about the radius of the black hole, in other words, the radius of the gravitational horizon corresponding to a particular mass fully contained within it. It is expressed by the equation:
This formula we derive easily on the basis of a secondary school mechanics (Newton's law of universal gravitation) and here we don’t need the general theory of relativity (based on it Schwarzschild derived this formula while approaching the matter with much deeper premises). We simply start with the equation for escape velocity (such as the second cosmic speed 11.2 km/s) and assume that the escape velocity is equal to c.
     If we substitute into this formula our estimated value of the mass of the Universe, we obtain the following value of the radius of its gravitational horizon: R = 15.6 billion light years. We can see that this value is similar to the value of the radius of the Universe which we calculated on the basis of Hubble’s law (fifteen billion light years, assuming H factor = 20). Almost exactly the same. Let’s note, however, that the possible equality of radiuses: R(grav.) = R(H) is not at all so obvious. H factor (and on its basis the Hubble radius of the Universe) is determined from direct measurement of the distance and relative velocity of specific objects, while the mass of the Universe (and hence the radius of the gravitational horizon) were evaluated on the basis of extrapolation of counts of visible objects, taking into account additional (estimated) correction for the mass of the non-radiating matter.
     But maybe it's just a coincidence? No! It's very unlikely, given the magnitude of the number (coincidence of such large numbers is almost inconceivable). The claim that this coincidence has always existed and is a peculiar feature of the Universe, is not devoid of rational sense. After all, we most probably do not live in some special time. It would be difficult to accept such a thing, unless we would refer to the unique malice of the Creator. He made a prank, did He? No, I personally (and I think all of us) do not suspect Him of it. Anthropomorphization of the Absolute? No! That would be the pinnacle of conceit, peak of self-deception.
     More reasonable is to accept (more modest) thesis that from Nature’s point of view this part of space-time in which we find ourselves is not unique. Already Giordano Bruno voiced that opinion (until 1600). No, I do not intend to be his incarnation. After all, we have accepted the cosmological principle. So let’s assume that this is not a coincidence, that there is something more in it; perhaps even an indication of some deep, fundamental truths of nature.     
     Let us assume that these radiuses are (even) identical, as the difference between the results of our calculations, which is in fact very small (the lengths of radiuses), may be caused by the method we used: the mass of the Universe was our rough estimate, while the H factor we adopted in an arbitrary manner without knowing its exact value, although on the basis of currently accepted estimates. So let us rephrase our conclusion in a more ceremonial manner: The gravitational horizon of the Universe coincides with the Hubble horizon. This equality and even identity is of a universal character. In other words, the gravitational horizon of a being with the mass of the Universe coincides with the “sphere”, which distance from the observer (no matter where he is located) corresponds to the invariant speed of expansion (c), which, as we know, is the upper bound of the relative speeds of objects (galaxies), as it is indicated by Hubble’s Law. We shall call this distance call the radius of the Universe. We'll see where this will take us.
     And what about the interconnecting horizon? It will probably leave the stage although today that’s the one that plays the main role. It can be defined as follows: It is the greatest distance from which photons can reach us today, kindly informing us about the presence of something somewhere there. This definition is absolutely correct if the Universe is infinite (in addition static) and, of course, if it never exploded.
   Let’s note on further reflection that the above postulated equality should not present any particular novelty, it shouldn’t even surprise. It is simply a natural thing. After all, the escape velocity from the black hole is equal to c, the same as the upper limit of the relative velocity of objects of cosmological significance (Hubble's law). And it does not matter where the observer is located... As one can see this equality is even consistent with the cosmological principle. Therefore, with the above postulate, in spite of the initial hesitations, I have not taken too great a risk. It's just a little percussion cup in comparison to a powder keg on which I sit. By the way, how comes that this has not been noticed before? [Maybe it was noted, but the thing did not fit into the system. What was needed was a boy in the crowd admiring magnificent robes of the king.]
      The culprits are the curvature of space and the related conclusion that considering the mass of the Universe as such, “does not make sense.” Humans are half-blind beings that see primarily what they want to see. I (as a human being) did not immediately notice this thing either. And anyway, I had it easier, because somehow I look at things a little differently. Just something got left in me from the times I was a schoolmaster. And at those times dealing with me wasn’t a piece of cake.  

    And here comes the doubt concerning our estimate of the mass of the Universe. The fact is that the number of luminous stars and galaxies has been and will be different at different ages. So our estimation smacks of naivety, since we want to learn about the invariant, omnipresent features of the Universe, independent of the time when we study them (apart from special circumstances, such as the very beginnings of expansion). We can be pretty sure that our time is not unique. How to reconcile this with a fantastic convergence of Hubble and gravity radiuses arrived at on the basis of counting the stars and galaxies, convergence which, one may think, is universal (?) Here it may be worth returning to reflection at the end of the previous section of this article, relating to the thermodynamic component of the total energy. I think, at least at this moment, that the primary as invariant, is the equality of radiuses, which constitutes the basis for (exact) determination of the mass of the Universe.
     An accident? If so, then not isolated. Nature helps the brave. It helped Hubble for example, who announced his law based on the insignificant number of data - more than a dozen galaxies. That was certainly not sufficient for this observation to be announced as a law. Of course, such an example is not any proof. What is sure in any case is that the “revealing observation” is verified by life. As it will soon turn out, equality of radiuses leads to the result consistent with the known ascertainments (not mine).
    As we will see in a moment, the just postulated equality of gravitational and Hubble radiuses of the Universe implies a different approach to the issue of the mass of the Universe. The mass of luminous matter, due to inability of its full evaluation, is actually the supportive concept. It should be noted, however, that its initial estimate led to an insight that gained the rank of a postulate. In what follows we express the mass of the Universe as a quantity directly resulting from the postulated equality, not messing up in uncertain measurements based on observation, among other things, mindful of the aforementioned thoughts. It's good when the data obtained from the study of local systems, allow for inferences on global features and enable verifiable generalizations.
     So we can combine the formula: v = Hr ... → c = HR, expressing the Hubble’s law with formula (1) for the gravitational radius. We get:
Specific calculations which we will conduct based on this, will enable us to decide whether indeed there is something in it, or whether it’s just a coincidence. Here's what we get: 
This definition of the mass of the Universe has nothing to do with the counts of galaxies or the content of deuterium, and at this point we do not consider the question of what this mass is composed of. So let's call it the Assumed Mass of Universe (AMU). From this moment on, speaking of the mass of the Universe, I mean just this CMU. In addition, let us note that we are talking about the gravitational mass, which with the passage of time, judging by the formula (2)... But let’s not get ahead of ourselves.  
     We will now conduct calculation which will answer the question: “To what mass correspond the dimensions of the Universe, calculated from the assumed value of H factor (20)?” Applying the formula (2) we get: M = 0.957·10^53kg. Calculate it yourself (not forgetting the units). I remind you that the value of H is estimated on the basis of observational data. Our findings fit very well with the mass of the Universe which we estimated at the beginning. If we accepted the value of H factor to be equal to 17.5 (middle of the range of values H, considered as possible), we would obtain: 1,085·10^53kg. As you can see the exact value of the H factor, as of now, is not of a critical importance, is non-essential to the crux of the matter. What’s the conclusion from all this? Well, the one that we are inside a black hole! We live, and we even discover such things! (And nothing rips us apart as in a nasty black hole with singularity. Actually, we could have anticipated it a long time ago. So to sum up, we can say the following. The Universe is expanding (it is already known from observation), and its size is determined by Schwarzschild’s radius (depending on the mass); and it is understood that if today, then at any time, because our time is not unique. What follows from here? it follows that...

3. ...The mass of the Universe is gradually increasing¹.
     After all, the magnitude of the mass directly determines the value of the gravitational horizon which increases along with the increase of Hubble radius.
     The mass of the Universe is increasing, is it? Is that possible? Can this be explained based on the current knowledge? Is it acceptable? So what is the mechanism of mass increase? That is the question. Let's try to find an answer. What immediately comes to mind is the Steady State theory, which creators were: H. Bondi, T. Gold and F. Hoyle (1948), quite popular in the fifties and early sixties of the last century. It assumed, among other things, continuous creation of matter out of nothing, which was to ensure stationarity of the characteristics of the Universe despite its expansion. This “out of nothing” finally buried this theory, even though it was not all that absurd, considering that it was a preliminary attempt to preserve the stability of the characteristics of the Universe, because “after all, it’s the Universe”; and considering today's multitude of ideas, no less interesting and accepted with deep, if not pious “understanding” as if the Philosopher’s Stone was just around the corner. Oh, to be Harry Potter, even for a moment... And by the way, not everything that exists must be visible.
     So what is the mechanism of mass increase? The answer should be definitely sought somewhere else. Let’s consider the following possibility. The Universe is expanding, which means broadening of the horizon. As if we watched from the rocket taking off or even from an ascending plane, seeing more and more extensive landscape, noticing new details, more and more distant from the starting point. This analogy suggests that we are talking here about the interconnecting horizon ****. 
If we look at the globe from an increasing distance, we would actually see the growing area. However, we would never see the whole globe. From an infinitely great distance we would see at most the area of a hemisphere. And what is further? Anti-world?... For the record, we find ourselves within the Universe. So do we therefore see everythingness?
    Horizon defined by invariant c is something else, since it creates an absolute boundary between being and non-being. [By the way, this does not preclude the existence of particles with superluminal speed - about this elsewhere] However, if this is an interconnecting horizon, something behind it certainly exists. By expanding, it encompasses spaces which were beyond our perception. We are joined by objects that so far, from our point of view, "did not exist". Are these new objects gradually increasing the mass of the Universe? What would result from the joining process? We should discover suddenly emerging objects, like novae and supernovae stars, although on the very horizon. Would we recognize this from very large read shift? Infinitely large? Not necessarily since it's not Hubble horizon but interconnecting horizon. So there emerge those whose light has just reached us. Where they emerge? For we know very distant objects that we have seen for a very long time. A little further than quasars? But no further than the horizon. Wait a moment. Objects that we are finally to see were there before, although we have not seen them because photons of these objects “were still on their way”. These objects existed at least since the dispatch of these photons. So their mass was already then a component of the mass of the Universe, since long before they were observed. So it's not about whether we perceive some extra matter or not, but rather whether it exists as an integral part of the Universe. Objects possibly just noticed (through photons), have nothing to do with what we are looking for. So would it be about the mass as if brought into existence? Again, we are reminded of yet utterly rejected steady state theory. The reason for doubting such an approach comes also from our determination that the gravitational horizon coincides with Hubble horizon, which implies that the mass of the Universe is increasing. And let us remember that the “visible” horizon is the Hubble horizon, which is the locus of points with invariant speed c. All concrete objects, galaxies, even the most distant are, of course, closer, drifting away at lower speeds and are visible today, if only potentially: we should just wait for better telescopes and remember that stars were formed not immediately after the Big Bang***** . All the (very distant) objects we detect due to the relatively high value of redshift. However, they already exist. Contrary to one of the paradigms accepted today by many physicists we cannot condition the existence by observability (!). In this context, clinging to the concept of interconnection is rather pointless, in any case, it does not explain the increase in the mass of the Universe.
     So what is the mechanism of this mass increase? We assume that all of this makes sense, because as yet we haven’t come to some logical contradiction despite the persistence of the habits of thought.

4. The mechanism causing the increase in the mass of the Universe
   “There is an increase in the mass of the Universe” - is the essential conclusion of the preceding chapter. Previously, we found that the material content of the Universe is limited (not infinite), even substantially invariant. The premise for this assertion is the accepted as fact occurrence of the Big Bang. So there should come the time when this “fun” will end because due to the limited amount of matter the Universe will run short of it. We'll come to the limit of the mass increase. What then? In this context the hypothesis that the Universe will start to contract seems logical. It is difficult to count on the fact that the expansion will suddenly stop. “All of a sudden? And what will come next?” Thus we have an oscillating Universe. Let’s note that we again reached this conclusion, and by starting from different premises than those in the first article on the cosmological principle, where I prioritised this very option of the development of the Universe. This confirms our (say mine) opinion concerning this matter. The hypothesis of such a Universe simply imposes itself. So we have yet another argument in support of the thesis of periodicity of spatial (maybe also physical) features of the Universe. So the arguments in favour of this thesis deepen. Thus we could draw the conclusion that, in half-time of the collapse, the mass of the Universe should decrease. Well, yes, but...
     So far we have estimated the mass of the Universe treating it as the value specifying the material (say: substantial) content. [Here we do not take into account the invariant thermodynamic component, which I mentioned at the end of the first chapter.] And here we’ve got a surprise. The mass increases, though I don’t think that there is an increase in the number of nucleons, electrons and other particles. So wherefrom this additional mass? [“In fact, it is about the Assumed Mass of the Universe” – but this is not too reassuring.] According to the earlier determination the Universe is everything, is the closed creation, so nothing comes from outside. We also reject the possibility of matter being created from nothing. Or maybe this extra mass is simply equivalent to energy? What energy? What energy increases with the growth in size, what energy is a function of mutual distance? We know that, it’s the potential energy.  Does it mean that this additional mass comes from the increasing potential energy of gravitational interaction of all objects without exception - from smallest to largest? Because from where else? This energy should therefore gradually increase due to the increase of mutual distance between bodies.  And was it always like that? Even when there weren’t any known to us nucleons and electrons? So what there was? In this context it is worth reminding ourselves of dual gravity, of Urela, the ending it phase transformation. I think that this is the direction we should follow to resolve the issue of mechanism causing the increase in the mass of the Universe.
     The mass of the Universe, as in fact the mass of each object, is the gravitational mass (according to the definition given in the fifth article). This mass increases with increasing distance between the components of the system, with the increase in the potential energy of the gravitational interaction between them. The mass defect decreases. Similarly the Universe. After all, its material content does not change. In this context the steady state theory can be calmly rejected. Thus, the increase in mass of the Universe is linked directly, we can say synchronized, with the increase in its gravitational potential energy... Easy to say...
     It sounds a little strange for those dealing on a daily basis with the general theory of relativity. The potential energy is not considered by the GTR. According to the concept preferred in this work, the space in the scale of material beings is rather not an autonomous, “primordial” being, a background for geometry changing stillness into “movement”. On the contrary. It is formed by relative motion of matter. Therefrom, most likely, its immanent (yes, yes ...) flatness. Here the “balloon” model is not adequate, and the flatness problem simply does not exist. As a result, the potential energy has here a specific meaning in spite of today's views. [By the way, this is not at all inconsistent with the possibility of a fourth spatial dimension, “responsible” for the specific topology of the Universe, the dimension (actually an additional parameter), which is about the periodicity of its features, both spatial and physical.] As it is known, these current views lead to two, classic by now, cosmological problems: the aforementioned flatness and the horizon (and these problems will be also soon de-problemised). This demonstrates the inadequacy of today's general approach to the immanent features of the Universe. Beggars can’t be choosers. The salvation for the Einstein-Friedmann concept, sweeping under the carpet these cosmological problems, was to come from Alan Guth’s hypothesis of inflation, which simply offends by its artificiality and typically human wheeling and dealing. On the one hand we have the quantum field theory, eschewing gravity which cannot be renormalized, and on the other hand the theory of gravity (GTR). It's only a modus vivendi, the Creator is not a bungler. As for the people... it’s a great adventure in search of Truth.
   We should add to this one more thing. According to the Friedmann equation a possible option is infinite expansion, in case of the development of the Universe according to the critical and open models. In this situation, consideration of the potential energy would cause additional trouble of the philosophical nature. While reaching towards the objective truth, infinity (and singularities) should be avoided.  
     In this work, as you can see, I deliberately avoid using the general theory of relativity as a base (I understand perfectly the inexcusableness of this approach). So as to be OK I would have to do nothing, proud (without any prodding) of the achievements of science. I'm proud of these achievements, but it is not enough. So (in my arrogance) I undertook an attempt to test the problems by means of conventional methods, though, what is important, taking into account the relativistic effects. Contrary to appearances, I do not reject GTR. However, I believe that this theory is so far incomplete: in case of astronomically macroscopic systems it works fine, but it is irrelevant for describing the Universe as a whole, which is more than it can take. [By the way, once again I warn against ontologisation of calculation procedures, which includes concepts of mathematical character.]
   I think that is should, for instance, take into account of the existence of mass defect. This can be the reason for a mismatch between Friedmann equations and cosmological reality, the explanation why, in relation to the Universe, GTR doesn’t meet expectations. It doesn’t, although as yet none of those who use it in cosmology have the courage to declare it openly. Declare? Realize. In general they dabble in mathematical modeling, proud of the excellence of their workshop. Here is one of the reasons that I decided to say my thing and approach the matter in an unconventional way.
   And how is it in the microworld? Gravity is simply not taken into account, allegedly because of its weakness. In this scale they ceded everything to quantum field theory, which does not consider gravity. Why it cannot be renormalized in calculations?... Certainly not because it is too weak in the scale of particles. Weakness, contrary to some, does not mean non-existence. That it cannot be renormalized in calculation provides quite a strong incentive for treating gravity not so much as an interaction but as a state (such or another) of the curvature of space-time. But that’s easy.
    And still deeper, in the scale of particle structure, gravity is extremely strong, and even forms the basis for all interactions (judging from my transgressions. See articles on dual gravity.). This alone constitutes a sufficient excuse to consider the option of its duality and in fact the reason for taking it into account.
     So I have restored to favour the potential energy. The concept of potential energy of the two bodies is widely known, and its definition is strict and unambiguous. However, when considering the potential energy of the Universe, talking about some bodies does not make sense. Besides, searching for a specific value of the total mass of all objects of the Universe also seems pointless. For this reason, in the third chapter I introduced the concept of Assumed Mass of the Universe (AMU). The same applies to the potential energy. So as to express it we will need to use that AMU. In addition, in the system (for example) of two bodies, this energy depends on the distance, is a function of their mutual positions. As for the Universe, the only universal spatial parameter is the value of the gravitational-Hubble radius. So in the context of our discussion we should present (not yet defined quantitatively) the Potential Energy of the Universe, treating it as a global parameter which value is a function of the global time of the Universe.
     The ideological basis for just such an understanding of matters is the firm belief (including mine), that the Universe had a beginning (at least in the sense of the start of a new cycle), that it was the beginning common to all the elements of its structure, that all objects share a common history. With the latter all seem to agree. And the Universe is an integral whole. Due to its expansion and continuous increase of the global potential energy, the global mass also increases (its deficit decreases). This can be written as follows:
according to Einstein's famous formula (E = mc^2). This time the increase of mass is directly related to the increase in size, because the increase in potential energy is generally conditioned by the change of position (a classic school example is tossing bodies up). Maybe we found the right track. In this context it is worth noting that this gradual increase in the mass of the Universe retains its condition, that is ensures (known observationally) “criticality” of development as it were in the nature of things, making the density parameter Ω = 1 kind of a universal constant, (or something that has become unnecessary). Worth remembering this sentence, even as a base for thought during further reading. This opens to us new horizons for further considerations, but of course does not release us from the “increase problems”, on the contrary. This idea of an increasing mass of the Universe, increasing, moreover, as shown here, I have never come across in written sources, constituting the standard basis for general cognitive awareness.
     “Naive cosmology”? Potential energy of the gravitational mass defect? What else? Modern cosmology simply does not focus its efforts on mass (and even less on energy), for reasons that we already know. Am I to be so terribly wrong? But the conclusions resulting from the adoption of this concept leads quite far, to unconventional, yet consistent, model of the Universe and its beginning (!), the model generating anticipations coinciding with the results of observations. And that’s the most important. We’ll see it further on. In this context, the models built on the Einstein-Friedmann equations may gain another practical sense (for example, educational). Is it really possible that this idea (of the increase in mass synchronized with the growth of the global potential energy) is the right one? Would this possibility be excluded due to its rejection based on the habits of thought currently in force? In any case (and for the time being) this idea is consistent with the presented here (that is in my works) fairly particular treatment of gravity.
     To sum up, we can say that the gravitational mass of the Universe (in accordance with the concept outlined here) gradually increases through the increase of its potential energy. This causes the decrease of mass defect of the Universe. According to today's views, its expansion in a natural way gradually slows down, and according to recent discoveries, something accelerates it. [It's not so much about changes of relative speeds, but about the change of curvature of space in conjunction with an increase in scale factor.] In this sense, the rate of expansion decreases (or increases). Without taking into account the dark energy this is compared with the deceleration of a body thrown upwards, although in this example there is a movement as such. Space in case of the Universe, and the actual movement in case of bodies... Not the best visualisation. Movement, or change in the curvature of space-time? As it can be seen, in the traditional approach (and in the example of a body thrown upwards) we have at the same time two fundamentally different approaches (actual movement + the curved space-time with changing scale factor, in relation to the Universe as a whole). Inconsistency? Well, uh, yeah, but this is only for the sake of visualisation. 

5. Reflections and thoughts in the context of estimations ofthe mass of the Universe,     or: let’s speculate
   Admittedly, the discussion of the mass of the Universe has any sense only if we assume that the Big Bang actually occurred. This is because if something explodes it cannot have an infinite mass, and the Universe simply oscillates. [From philosophical point of view, the explosion itself, all of a sudden, followed by the endless expansion is a serious problem, which cannot be downplayed. For avoiding philosophy cosmologists - there is no problem.] I have already drawn attention to it before. The mass of the Universe (no matter how it is defined) is therefore limited, is of a specific magnitude, no matter how great. So it makes sense to deal with the mass, despite its extensiveness. In particular, we have here a very interesting question: "What will be the maximum mass of the Universe at the moment of inversion between expansion and contraction?" My preliminary estimate (as of today) is of the order of 10^63kg (in relation to today's unit values).
     And here comes the problem. Each specific real number, except zero, is an element of an infinite set of equivalent numbers in the context of the fact that they have to express specific characteristics of a definite natural being. All of them equivalent to each other. “So why the maximum mass of the Universe is such, and not another?” [That is not infinite, results from the postulated cyclicality, existence of oscillations (and of course from the fact of the occurrence of Big Bang).] Totally natural question, given that we expect the Universe to be vested with features of a unique, fathomless ideal, and that is built according to the unequivocal and objective laws of nature. This global amount should indeed exert its influence on the measurable general characteristics of the Universe, and at the same time it should be validated by the values of universal constants. In particular, there should be some relationship between dimensions and variation of global mass and the value of constant G. Although this is speculation, it is worth to think about it.
   And now, giving (still more) rein to imagination, one can think that either there is a number other than zero, a very large number, and, just as zero, the only one, or there are infinitely many universes forming a continuous mass spectrum. If we include the necessity of existence of a specific structure and the complexity of such a creation, and therefore the existence of restrictions as to its minimum size, the matter gets complicated even more. So it is probably better to find that single number, perhaps representing an end of counting justified by need. Or, simply, the maximum mass at the time of inversion is precisely this unique number. But there are more of such exceptional numbers – such, for instance, as universal constants. The maximum mass would be one of them. We’ll have to wait a little before it’s determined. To whoever determines it I promise the right to call it by his/her name.
     First, however, we should probably find the period of oscillation. And we’ll deal with it in later articles, which does not mean that we will find it, but we’ll get some clues.
For now, let us note once more that the speed of expansion is equal to c. And remember that this is also the speed of light, the speed of photons. Physically, it’s about completely different kinds of thing. But these speeds are equal. According to cosmological principle, the speed of expansion is equal for any observer, which means that it doesn’t depend on the reference system. It is also the upper bound of the relative speeds of massive bodies. And what about the speed of light (electromagnetic waves)? It was assumed (as a postulate) as invariant. The special theory of relativity was created on the basis of this invariance. It anticipates, among other things, the existence of the upper limit of speed of material objects, including distant galaxies. And here we meet. But this is not the end. What does the speed of electromagnetic wave have to do with the speed of expansion? This is definitely not an accident. It is quite possible that the electromagnetic interactions appeared just at the moment when the speed of the expansion settled at the value c. [If that’s right, then we have one more argument for the thesis that the Big Bang actually took place (ignoring other weighty reasons).] Earlier, as we already know, there was Urela ending the phase transition. Thus c speed is the relic from the beginning of Hubble expansion, and from the moment when the electromagnetic interaction came into being. So we have the explanation of the meaning of such an astounding fact as invariance of the speed of light. A hundred years ago it was a postulate, and today, thanks to my fantasies, is the obvious conclusion, directly resulting from the cosmological principle. As you can see, this thread from time to time comes back in my essays. Am I repeating myself? No harm, because it's quite important. Apart, each of these essays are basically separate entities.²
The problem of saturation
   We found that the dimensions of the Universe gradually increase, although they are limited. Beyond the horizon there is not even space, because the Universe is everything. The existence of anything beyond the limit of the horizon would be even contrary to the cosmological principle, if only because the area beyond the horizon would have to have completely different characteristics than our Universe as we know it. This would be also demonstrated by the parameters of the relic radiation. This should mean that despite the non-zero global gravitational mass there is no external field. The Universe is, in a sense, gravitationally saturated. How to digest it? First of all, it is worth to confront this reflection with the content of the sixth article, which deals with planckons. But this is not a calming bath, on the contrary. The Universe is not a photon.
     Or is saturated - invisible to the objects possibly existing outside of it, other universes, or nothing beyond it actually exists, and the saturation as such does not apply to the case. Does this cover all the possibilities? We cannot see the other universes, because no signal from there can penetrate the horizon of our Universe. [It is difficult to treat the Universe like an ordinary black hole.] Also, no signal can be sent beyond the horizon. We do not disclose our existence just as they don’t disclose their. So around us (the Universe) there cannot exist a gravitational field. Thus, the Universe is the gravitationally saturated object, and this implies an assumption, maybe even the conclusion that it is also saturated with the amount of matter - it can contain neither more nor less.
   And yet it has mass. It has positive mass as well as negative potential energy, so we have zero – we’ll talk about it further on. Maybe that's why it is saturated (?). The question of zero gravitational mass of a system of material points was already discussed in the first part of the fifth article devoted to the duality of gravity. Yes, but what makes the Universe an object saturated in the likeness of a photon (the mass of a photon is equal to zero), although according to our estimate, its mass is not at all zero? The Universe is not the photon (“total mass-energy equal zero” - see above). With these statements I blurted it out. Because there is much to go on, but let's go back to the original line of thinking.
Once upon a time, long ago, the Universe was (still) so compressed that its gravitational mass was equal to zero. Not now, of course. Despite the comments above, I persistently ask: So how can it be saturated? Is it because there is no existence beyond the Universe? Can we make this assertion a priori? There is still a long way before we close this matter. Or maybe “saturation” does not necessarily mean zero gravitational mass, and the magnitude of the mass of the Universe does not affect it? In addition, if it (this saturation) exists, then it takes place all the time, from the very beginning, always, in every phase of the oscillation of the Universe. Here, let us remember the cosmological principle. It implies that the intensity of cosmological gravitational field at any point in space is equal to zero, because due to the uniformity of the Universe, forces acting on any given body from opposite directions balance each other out. And for that to take place, the Universe does not have to be infinitely large – which could result from full compensation forces (cosmological principle). The case of absolute balance of forces is resolved by the specific (still unknown) topology. [I am writing this with the full knowledge that invoking something unexplored is not an argument (and can be associated with a razor), it only indicates the possible direction for further investigation.]  Soon we shall see, for a change, that the potential of the global field is constant, not necessarily zero, and it is everywhere the same. [It reminds very much an electrically charged conductor (under electrostatic equilibrium)]. Saturation despite the existence of gravity... Is it possible? Soon we’ll give some thought to gravity of the Universe.
   This, however, raises the question whether the gravitational potential of the Universe has some value outside of it. That’s how it is with a charged conductor. In the context of our considerations the answer can be only one: the Universe is everythingness, so the question does not apply to the case. The problem of saturation would deepen the thesis that there is no existence whatsoever outside the (observable) Universe.
     Or maybe the reason for this saturation is some determined, yet unknown to us topology of the Universe as a whole? Where is the cause of this topology? Is it somewhere deep in the “sub-dimensions”? It is interesting that the space in the “middle” is flat, Euclidean (more about this in consecutive articles), and outside... It is possible that this “outside” does not exist. But let’s not get ahead of ourselves. So if outside no field informs of our existence, then the Universe cannot be visible to “colleagues”, it does not exist for any outside observer. For its inhabitants is therefore the only existing, even if it is an element of infinite multiplicity. This plethora is known only to scientific fantasists. If This One, then also other Universes from an infinite set (either one only or infinitely many) are not visible. So for an “objective” observer who is “outside” there is only the infinite emptiness. Then what he is doing there for heaven’s sake? Is there a sense for the existence of an infinite emptiness? For the existence of an infinite Nonexistence? That this nonexistence may be apparent, false: full of energy “False vacuum”? Or that the Explosion, and therefore the Universe, is a bubble locally created from infinite energy, and that there is infinity of such bubbles – universes? An attractive fantasy - is not it? But ... What's that got to do with our problem? Will it help us understand our Universe? In addition, our existence bears absolutely no influence on the existence (or nonexistence) of something outside of us. 
   This alone leads to the conclusion that what we perceive as the Universe, is the uniqueness and Everythingness at the same time and at the same time is quantitatively limited. The observational fact indicating the correctness of such a view is the known to all, without exception, fact of the night sky blackness. Interested (and a little less informed) can read about the so-called Olbers’ Photometric Paradox. The thesis of saturation and quantitative limitations of the Universe will come up many times in this work. And by the way, in connection with non-zero mass and saturation, something will already emerge in the Annex to the first article on the neutrino particle. As for now...
   ...turning back to the Universe, most likely gravitationally saturated, we can assume that even if there was an infinite multitude of other universes, their discovery is not be possible, because, as we can suppose, they would be also saturated, not letting us know about themselves. A material system pretending to be the universe (one of the infinite number of them) should be large enough to comply with the cosmological principle, and thus should be saturated. The larger the object, the closer to saturation. Why would we have to stand out? If someone still doubts, let’s look at it from another angle. The detection is not possible not because everything that we see is part of the Universe, according to the definition of the concept. If there are objects that do not belong to our Universe, they should be breaching known to us observational patterns: the cosmological principle, and, of course, the Hubble’s law. So far nothing points out towards the possibility of making such a discovery, even towards any sense of such expectations. Although... it’s strange what is happening in connection with the existence of the Great Attractor... The conclusion would be that either different universes cannot penetrate each other (as for example, in a collision of galaxies) or their parts cannot be mutually detectable, due to differences in their physical characteristics; or else the whole absolute material and spatial everythingness is the Universe open to our perception. Personally, I prefer this to an infinite number of undetectable entities. Not only for practical reasons. And what about the Great Attractor? Some explanation will be found.

Á propos
¹) Or maybe this independence of equal radii from time (and the current appearance of the Universe), this universality, means that the units of measurement themselves gradually increase with the expansion of the Universe? So there are no more kilograms despite the gradual change in brightness, despite the gradual increase in mass. This is possible if all the changes occur in absolutely each scale – down to Planck’s. It's as if in terms of global measurement the Universe was static. However, it would be a “dynamic staticity”. The units of measurement would change in such a way, for example, that numerically the mass of the Universe would be always the same. Is this a correct conclusion? We'll see further.
    Let’s suppose that the values of units of measurable entities are constant. We can do that, since the system of units cannot decide on basic matters. The fact of measurement and type of units used, cannot affect the objective characteristics of physical systems. [Yes, yes, quantum mechanics, observable, uncertainty...] In this cosmological context, I agree with Einstein's famous statement: “If I do not look at the sun, does it mean that it does not exist?”
     Following this consideration, we can however say that this “staticity” could be directly related to the invariance of the general laws of nature - the independence of these laws of the place, time and scale. Time, obviously, exists, and it is proved by the existence of variation, evolution. Evolution, however, would be demonstrated only by the given to observation local changes – up to inversion of the Universe and beyond.
     Would that imply a change in the values of the universal constants? There is no basis for such a view (at least for now), if only in relation to what I stated a moment ago (the underlined sentence). After all, any permanent changes would have to be of a global character. This concerns in particular the gravitational constant, which changes I exclude, since planckon constituting the quantum of gravitational field, and at the same time the absolutely elementary being, cannot be something variable. The question of any changes in the parameter c I have already addressed a number of times, and I will still come back to it.
²) And another connotation. As we know, in our environment the particles of the microworld move (and as a matter of fact, it's not about accelerators) very fast, even with relativistic speeds. With the same speed move very distant galaxies. This alone says something. [Actually, why natural speed of particle is so high, having nothing to do with the relative speed of objects that surround us? Or maybe this is related to the history of the origins of the Big Bang? Perhaps. We have to admit that the magnitude of this natural speed is significantly influenced by (relatively strong compared to gravity) electromagnetic and nuclear interactions, in which these particles are directly involved. However, I get the impression that this is not all. Does anyone share my uncertainty?] And now, if a particle originally belonging to the now distant galaxies, in its inert motion headed toward us once upon a time and reached us, then it should have exceptionally large amount of kinetic energy. Indeed, such particles were detected in cosmic radiation. Already some years ago, in a KASCADE experiment (Germany), with the participation of Poles, there were obtained (in the atmosphere) cascades of multitudes, even millions of secondary particles resulting from collisions of the particles of cosmic radiation, having an extremely high energy, with particles from the atmosphere. Their kinetic energy is estimated to be 10^19 eV. By the way, these particles are so fast that their speed is almost invariant. They are relatively rare. It is believed, I think rightly, that they are extragalactic components of corpuscular cosmic radiation. In addition, in accordance with the above stated supposition (and of course with the cosmological principle), these particles should arrive from everywhere. They should create a homogeneous and isotropic corpuscular radiation. This thing should be examined. (For now) we do not know where they acquired that huge energy. There are various hypotheses, more or less feasible. Now we have one more - see the beginning of this reflection. 

*) Extensive parameters – proportional to the amount of matter in the system: mass, volume.
Intensive parameters – independent of the amount of matter in the system: temperature, pressure, density.
**) Megaparsec is million parsekcs. 1 parsek equals to 3,26 light years.
***) According to presumptions signaled in the literature of the subject, already after 200 million years. It is about the stars forming from fluctuations in density in a very limited scale, still before separation of systems which were to transform into galaxies - objects that we can see. They should be star with an extremely low content of metals (elements heavier than lithium). The vast majority of those of them that have survived to this day are certainly advanced stars in evolutionary terms. Let’s note that in those distant times matter was very highly concentrated. So many stars came into being. The mentioned in the text number of 1.5 billion years applies to pre-galactic objects which can be observed by means which we already have. It is mainly about quasars, seen thanks to very intense energy transformation occurring in them.
****) Coordination of properties and processes cannot proceed at a speed greater than the speed of light. Regarding the situation described here, the given object, as I already pointed it out, can be seen only after the time it takes for light to get from it to the observer.
*****) This is not fully compatible with today's interconnecting understanding of the issue: “we see because of photons that have reached us”, which does not take into account the fact that with this, “once upon a time, billions of years ago, we were all together.” I will devote a lot of space to this issue in the following articles.