- If the density of the Universe is less than the critical density it will expand forever
- If the density of the Universe is greater than the critical density, then gravity will cause to collapse back on itself in a "Big Crunch"
If they are equal, the geometry of the Universe is flat (Euclidean)
The total density is equal to the critical density (exactly, up to measurement error) and experimental data from various independent sources confirm that the Universe is (most likely) flat. And (most likely) it will continue to expand forever.
- Dark energy seems to accelerate the Universe's expansion. Relevant explanation from here:
With dark energy, a spatially flat universe is still on the boundary between closed and open, but if there is enough dark energy, the expansion of the universe accelerates, and the universe can expand forever, even when it is closed.
Do you know if there is a hypothesis that proposes a cyclic model of the Universe in which either its density is decreasing or its critical density is increasing (or both) in (finite) cycles?
Couldn't that explain why the total density seems to be exactly equal the critical density?
So for example if density decreased by the smallest possible amount after each Big Crunch it would have collapsed every time until a Universe came into existence (Big Bounce) that lasts forever (until the Big Freeze or alike at least). Maybe per the anthropic principle that could have also been required for life to exist e.g. because the Universe would have collapsed before otherwise?
Update: is this paper relevant (how)?: "A new kind of cyclic universe":
a novel cyclic theory of the universe in which the Hubble parameter, energy density and temperature oscillate periodically, but the scale factor grows by an exponential factor from one cycle to the next. The resulting cosmology not only resolves the homogeneity, isotropy, flatness and monopole problems [...]