<p>The Big Rip happens if the equation of state for the dark energy has <span class="math-container">$p/\rho = w&lt;-1$</span>, and all empirical data give us <span class="math-container">$w\approx -1$</span>. A Big Crunch requires a pretty high value of <span class="math-container">$w$</span> (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.</p>

<p>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 <span class="math-container">$w$</span> moving across the Big Rip boundary. </p>

CC BY-SA 4.0
2019-06-03T21:48:31.097Z
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%.
curious_cosmo
CC BY-SA 4.0
2019-06-04T08:09:55.317Z
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.
Anders Sandberg
CC BY-SA 4.0
2019-05-31T09:30:57.200Z
2019-06-02T12:45:49.473Z
2019-06-02T12:45:49.473Z
Anders Sandberg
<p>If the dark energy equation of state <span class="math-container">$\omega$</span> evolves with time, and becomes larger, this would result in decelerated expansion and eventually a Big Crunch. If <span class="math-container">$\omega$</span> 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).</p>

<p>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 <span class="math-container">$\omega$</span> evolves in under a quintessence model?</p>

<cosmology><expansion><dark-energy><fate-of-universe>
Has the Big Crunch been ruled out?
curious_cosmo
# Has the Big Crunch been ruled out?

(Asked by: username_0 on 2019-05-30)

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?

**Tags:** cosmology, expansion, dark-energy, fate-of-universe

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## 1 answers

### Answer by username_1 on 2019-05-31. Score: 4 | Accepted answer

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.

> **Comments:**
> **username_0**: 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%.  
> **username_1**: 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.  

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