• 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 [...]


1 Answer 1


Various cyclical cosmological models have been discussed at various times: https://en.wikipedia.org/wiki/Cyclic_model Tolman used thermodynamics to rule out the most straightforward ones in 1934. There is currently no promising-looking model of this type that doesn't involve a lot of very speculative and unproven physics. Various proposals of this type, such as Penrose's, turned out to be inconsistent with observation or with other known physics.

Couldn't that explain why the total density seems to be exactly equal the critical density?

No, in a cyclical universe we would expect the density to be greater than the critical value.

  • $\begingroup$ Didn't expect any unspeculative theory of this sort. I'm just asking about whether a hypothesis of this type exists at all. For example a LQC-related hypothesis could be interesting I think. Maybe this paper is relevant?: arxiv.org/pdf/1812.06841.pdf My question is about a cyclical model in which the density is greater than the critical value (as expected) until it is equal the critical value and the cycle stops. Or did you mean to say that it's likelier to only appear equal? I'm also interested in hypothesis that have a parallel element instead of only a sequential one. $\endgroup$
    – mYnDstrEAm
    Oct 24, 2019 at 19:58
  • $\begingroup$ User4552's objection to Penrose's "Conformal Cyclic Cosmology" (described in his 2010 pop-sci book titled "Cycles of Time") may be valid, because the astronomical procedure Penrose had suggested for its verification was widely criticized. His model suggested reiterations on expanding scales, and avoided the increases in the density of entropy that Tolman had found his own model to require: If Penrose's work would've been theoretically unsound, I doubt he would've been selected for a 2020 Nobel Prize, but proofs of cosmological models involve hitting a jackpot if the universe is big enough. $\endgroup$
    – Edouard
    Mar 11, 2021 at 21:22

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