# Has the Big Crunch been ruled out?

If the dark energy equation of state $$\omega$$ evolves with time, and becomes larger, this would result in decelerated expansion and eventually a Big Crunch. If $$\omega$$ decreases with time, becoming more negative, then a Big Rip would occur. I understand that the Big Rip has not yet been ruled out by current observations, but I often hear that the Big Crunch has been ruled out since we know the universe is expanding (and accelerating).

If the Big Rip can't currently be ruled out, then how can the Big Crunch be ruled out? Shouldn't they both still be on the table, unless we can somehow infer which direction $$\omega$$ evolves in under a quintessence model?

The Big Rip happens if the equation of state for the dark energy has $$p/\rho = w<-1$$, and all empirical data give us $$w\approx -1$$. A Big Crunch requires a pretty high value of $$w$$ (it must go above -1/3 to just stop the acceleration), but of course if dark energy is changing over time it might do that.
So tentatively ruling out Big Crunches is the reasonable thing to do given observational evidence and the assumption that the future will not be wildly different. If one thinks we should be more open to dark energy changing (which is going to be rather unconstrained by observation for the foreseeable future) then we should also be more open to $$w$$ moving across the Big Rip boundary.
• How strict is this $w < -1$ cutoff for a Big Rip? For example, would $w = -1.04$ lead to a Big Rip? I ask because I believe the current uncertainties on $w$ are about 4%. Commented Jun 3, 2019 at 21:48
• Yes, it is a strict cutoff. The scale factor in FLRW grows like $a(t)\propto t^{2/c(1+w)}$ when $w\neq -1$, and for $w<-1$ there is a singularity at some point in time. Commented Jun 4, 2019 at 8:09