Suppose that cosmological many-body clustering runs on forever. What will happen in the infinite future?

Standard Einstein–Friedmann universes suggest three main possibilities. If the Universe is closed (Ω0 > 1, k = +1) and recollapses into a singularity, all large-scale structure will eventually be destroyed in the big crunch. Whether anything can be resurrected from surviving seeds if the crunch is incomplete (Saslaw, 1991) is unknown. Oscillating universes are possible, though in practice we do not know if the physical requirements for repeated oscillations are consistent with reasonable equations of state. Oscillations whose amplitudes were too small to produce equilibrium would accumulate the debris of previous cycles. Quite apart from the question of increasing entropy, such models would probably require especially fine tuning to produce our observable Universe.

If the Universe is open and expands forever with negative curvature (Ω0 < 1, k = –1), it will expand so rapidly after redshifts z ≲ Ω0–1 (see 30.13) that new larger structures will generally cease to form, and the largest scale patterns at z ≈ Ω0–1 will be essentially frozen. These patterns then tend to expand homologously, becoming increasingly stretched and dilute in physical space: Pascal's nightmare. In models with a cosmological constant, the expansion may pause. But it will have to be carefully tuned, so the quasi-stationary period does not produce overclustering, and also satisfy other constraints.