Assuming the mass of the universe was spread completely evenly throughout space why would gravitational attraction happen? All bodies in the universe would feel gravitational tug equally in all directions so why would they go anywhere?
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5Does this answer your question? Why isn't an infinite, flat, nonexpanding universe filled with a uniform matter distribution a solution to Einstein's equation? – PM 2Ring Jun 28 '20 at 23:38
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see https://www.youtube.com/watch?v=vKLqWj0FRyc&t=058s&list=PL7Yaf7nQHP3DSNGnCWvQOgz5A_EtQ-6sr&index=6 – Yukterez Jun 29 '20 at 05:39
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The question seems to assume Newtonian gravity, not general relativity – Charles Francis Jun 29 '20 at 18:05
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@CharlesFrancis True, but most of the answers to the nominated duplicate target also cover the Newtonian case. – PM 2Ring Jul 01 '20 at 01:38
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If one assumes the question in Newtonian dynamics (as distinct from gr) then the answer is that Newtonian gravity for an infinite uniform matter distribution in flat space is inconsistent. This can be shown from the equations of Newtonian gravity, in which the problem is that the integrals over all space do not converge, but a simple argument can also be found from Newton's shell theorem.
Let mass density be constant, $\rho$. Take any two points, $\mathrm A$ and $\mathrm O$, a distance $R=\mathrm {OA}$. According to Newton's shell theorem the gravitational force at $\mathrm A$ due to any spherical shell containing $\mathrm A$ and centred at $\mathrm O$ is zero. The gravitational acceleration due to matter inside a sphere of radius $R$ centred at $\mathrm O$ is $$ \frac {4\pi} 3 G \rho R $$
In other words the gravitational tug does not cancel out, but is towards $\mathrm O$, which is clearly inconsistent because $\mathrm O$ can be any point in the universe.
Charles Francis
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