# Critical density of the universe (no, not that one)?

I seem to recall reading something that said if the density of the universe was off by as little as one atom per cubic meter, the universe, as we know it, would not exist; one less and there wouldn't have been enough gravity to form galaxies and stars, one more and there would have been too much matter. (I don't know (or remember) what would have happened in the case of too much matter.)

If I Google the title of this question, all I get is stuff about the expansion of the universe, nothing about whether or not it would exist. I've tried other variations but can't seem to find anything.

Did I grossly misinterpret this? If not, does anyone know of any articles that can confirm or refute this?

• The key to your statement is that the universe as we know it would not exist. The universe would still exist, but if the density was a little higher, things would be much more clumpy, because gravity would pull them together. If the density was a little lower, the expansion of space would pull things apart before they had a chance to coalesce, so the universe would be much more empty. Dec 21 '17 at 20:36
• The question of critical density is closely related to the expansion of the universe only, and not it's existence. Only at best half-informed sources would write something like 'then it wouldn't exist'. Dec 21 '17 at 21:17
• I did use the clause, "...as we know it..." I didn't say the universe wouldn't exist in some form or another. Certainly, some sort of a universe would exist; it just would've been very different than the one we see today, and most likely would not have been able to support life. Dec 21 '17 at 22:46

If the initial density of the universe could take any value, it would seem extremely surprising to find it so 'finely tuned' to the critical value $\rho_c$. Indeed, a very small departure of $\Omega$ from 1 in the early universe would have been magnified during billions of years of expansion to create a current density very far from critical. In the case of an overdensity ($\rho > \rho_c$) this would lead to a universe so dense it would cease expanding and collapse into a Big Crunch (an opposite to the Big Bang in which all matter and energy falls back into an extremely dense state) in a few years or less; in the case of an underdensity ($\rho < \rho_c$) it would expand so quickly and become so sparse it would soon seem essentially empty, and gravity would not be strong enough by comparison to cause matter to collapse and form galaxies. In either case the universe would contain no complex structures such as galaxies, stars, planets and any form of life.
To explain a bit more, the basic idea is that the universe will have started out with a more-or-less homogeneous and isotropic distribution of matter with some density $\rho$ (this is a pretty strong assumption in its own right, and worth addressing in a completely different answer). Note that the overall curvature of the universe is directly tied to this density so you may see some sources talk about this in terms of curvature instead of density. The main point, as described in the quote above is that the evolution of the universe, i.e., the ability for galaxies, stars, planets, life, etc. to form, is dictated by a critical density, $\rho_c$. If $\rho = \rho_c$ (or as close to equal as to be insignificantly different), our universe can form as it is now. The flatness problem comes into play because the Big Bang Theory implies that if the universe did not start out with (almost) exactly $\rho = \rho_c$, it would have veered far off course from our current universe and resulted in either a Big Crunch or a Big Rip.
This idea poses a really big problem for the Big Bang Theory because it requires such a precise setup for our universe, where any betting person would've said there's no way the universe could've started out with $\rho=\rho_c$. The main resolution to this problem is by introducing inflation into the model. The main idea here is that the Universe may or may not have started out with $\rho = \rho_c$, but so long as it was close enough, the hyper inflation at the beginning of the universe would have forced the difference to be so small as to be effectively zero, negating the effects described in the quote above. Another potential, and not necessary mutually exclusive answer is found in the Anthropic Principle, which I won't delve into here.