Can a theoretical object exist as such that its mass overcomes gravitational collapse A daydream the other day led me to the question if "a universe filled with water (or any other substance for that matter), instead of being mostly void" could exist within the rules of our current one.
I set on a Google journey to try to figure things out myself but I quickly hit the upper boundaries of my understanding of physics.

Now I am well aware that after a certain point, objects collapse under the force of their own gravitational field. Also something something about the Schwarzschild radius and 3 solar masses.
Extended to infinity and relative to its radius, the mass of the object has a cubical growth rate, while the force of gravity drops off at a square rate (does Newton's law of gravitation apply here?). Clearly the extra mass should overpower the gravitational decay, ultimately leading to a collapse.
I presume all this has to do with all points inside the object being attracted to each other and that there is a center of the mass.
This is where the original question kicks in - what if the object was so ridiculously big, or even better - infinitely big, that there was no single center of mass.
Would a "structure" like that hold? Will another object floating inside experience weightlessness as it is being pulled with an equal force from every direction? What weird relativistic effects would arise from the fact that even if the pull cancels out, it still exerts an infinite force?
 A: An infinite "universe full of water" is actually very close to how the real universe is typically modeled, except that instead of water it's the right mix of ordinary matter, dark matter, radiation, curvature and cosmological constant. On large scales it's reasonable to assume that the density of each component is everywhere equal at a given time. And indeed, depending on the density you put in, the universe can expand forever, or else recollapse for high enough density. The density for the boundary case where the universe barely avoids recollapse is called the 'critical density' (the rest of that article is also interesting the context of this question, though I link to a particular section).
I won't go into much more detail here because this is a standard topic in any cosmology class, so it's covered in extensive detail in various books and articles. The keywords you want are 'critical density (of the universe)', 'Friedmann equations', and 'Friedmann-Robertson-Lemaitre-Walker (FRLW) metric' - for this last one note that the order of the names often changes depending on the author, or sometimes one or two are omitted.
By the way, there's no global "centre of mass", as a search for questions about the centre of the Universe on this site should reveal in some detail.
