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In this PSE post the issue is about the stability of an infinite universe under Newtonian gravity.
Here I'will drop the Newtonian constraint because we know of the finite speed of interactions and I ask:
How can someone explain the existence of a gravitational collapse?

In the drawing the universe is isodense and infinite and it will extend outside of the limits of the screen ;)
The grayed spherical regions represent the observed universe in relation to the points A,B,C (that can be considered as centers of the universe) and the three points are causally disconected because it is impossible that the interactions had time to propagate from A to B , ... to the entire universe.
You can imagine a similar region around the point X that can see both A and B.

Because nowhere exists a gravitational gradient, whatever the density, there is no chance of motion whatever the selected point. IMO.

How can someone explain the existence of a gravitational collapse?
enter image description here

Qmechanic
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Helder Velez
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  • Does noting the non-uniform mass density of our universe have bearing on your question? – BMS Apr 19 '14 at 06:15
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    @BMS non-uniformity reported in what observations? I forgot to add isodense ;) as observed. – Helder Velez Apr 19 '14 at 06:39
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    some will be tempted to point that FRW eqs show that it can grow/collapse at will. That is out of focus because they posit: It also assumes that the spatial component of the metric can be time-dependent. No wonder that under this additional injection the eqs will have to show whatever we wish. Without this additional constraint the universe will not collapse. Thats my point. – Helder Velez Apr 19 '14 at 21:27
  • Since I posted the question I got two downvotes elsewhere without any comment, as usual. Arguments are much more difficult than downvotes. Those esteemed downvoters did not realized yet that I do not care about that. Please use some arguments. I do care. – Helder Velez Apr 19 '14 at 21:59
  • I can only guess why people are down voting this question, but I find it enormously unclear. I suspect that you have a big structure of interconnected ideas in your head and that this might make sense in the context of those thoughts, but no one in your audience is coming from that perspective. This is a common problem in technical writing especially where there is pressure to be concise. – dmckee --- ex-moderator kitten Apr 19 '14 at 22:26
  • The constraints are very clear and have the same definition everywhere: infinite universe, isodense and a finite speed of gravity. No one complained in the other linked post in relation to the same terms. The drawing is confusing ? Do I have to beleive that there is a gravitational collapse whitout a convincing argument? That is the most simple universe we can define, flat, infinite (or large enough) and isodense (at least at large) as the one we observe when we look back in time. Someone can put motion on it without an explosion? Can you be more specific? What term/condition is unclear ? – Helder Velez Apr 20 '14 at 01:36
  • in this setting there is no gravitational collapse. the problem is that most textbooks and papers on cosmology change their assumptions every now an then within the text. I guess the downvotes come from one of those authors ^^ upvote from me ;) – image357 Mar 28 '15 at 19:41

2 Answers2

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Also in simple terms. In a universe that is infinite with a uniform distribution of dark matter you are always in the center of that distribution. Gravity in a spherical shell, if you work it out, always goes to zero inside a spherical shell. This is why gravity in the earth doesn't go to infinity. Approaching the earth gravity increases with distance by 1/r^2. However, when we reach the earth and pass through the outer spherical shell of matter, the gravity from that shell now cancels. The volume of that matter decreases as a function of r^3. The result after you do the math is a linear decrease in gravity till it goes to zero in the center of the earth. An infinite universe of evenly distributed matter with no defined center contributes zero gravity everywhere because you are always in the center of a sphere. This might make us question if such an infinity can truly exist.

Now let us acknowledge that in an infinite universe with time lag of information the observer is exactly in the center of sphere for their information. If they move the center of their sphere of observation moves with them. This would suggest zero gravity contribution. On the other hand, can we statistically assume an even distribution of anything when there is a chance in said universe that density might not be perfectly distributed? Perturbations in density then lead to further disturbance in gravity cancellation.

Dustin MacDermott
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  • flat, and large. http://www.dailygalaxy.com/my_weblog/2013/02/the-real-universe-is-250-times-bigger-than-the-visible-hubble-volume-todays-most-popular-1.html – Helder Velez Dec 26 '14 at 13:13
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    "This might make us question if such an infinity can truly exist." ---> why? – image357 Mar 28 '15 at 19:59
  • Perturbations in density (excess) will not give a gravitational collapse because it can be shown that any excess of density above average will be erased (contrary to consensus belief) and any defect of density will grow an enormous void. – Helder Velez Mar 28 '15 at 21:38
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    The gravitational field is only zero inside of a hollow spherical shell, or in the exact geometric center. – Zo the Relativist Jun 02 '15 at 14:24
  • Note that the "linear increase" in gravity inside earth is only true if you assume uniform density. – Kyle Kanos Sep 30 '15 at 10:14
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In my previous answer I argued that a truly infinite universe that is density that homogenous and isotropic can not collapse gravitationally if the universe has lasted for a finite amount of time.

However the equilibrium state I described is not realistic because it is unstable and requires the distribution of mass to be perfectly homogenous not just on average on large scales, but at the atomic level. Even one particle out of place starts a local collapse and a chain reaction that spreads outwards causing collapse globally. Quantum mechanics and the uncertainty principle dictates there would random fluctuations and it would be impossible to maintain a perfect homogeneity and equilibrium and the probability of having initial conditions with perfect distribution is practically zero.

KDP
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