B If the Universe keeps expanding this way, it gets torn apart

[A Middle Aged Man]

TL;DR Summary

the universe keeps expanding until it tears

The expansion of the universe is accelerating. So the big rip is the best bet for how it ends isn't it? This fellow seems to think so:



I guess the heat death is not the most likely, unless new evidence shows otherwise.

 

[PeterDonis]

The expansion of the universe is accelerating.

Yes.

So the big rip is the best bet for how it ends isn't it?

No. Accelerating expansion does not mean the big rip happens.

This fellow

It is not a good idea to try to learn science from YouTube videos.

 

[A Middle Aged Man]

But if the expansion is accelerating why wouldn't it just keep going until it ripped? What would prevent it from doing anything else?

 

[PeterDonis]

if the expansion is accelerating why wouldn't it just keep going until it ripped?

Because that's not what accelerating expansion does. For a big rip you need something more than just accelerating expansion.

What would prevent it from doing anything else?

The fact that accelerating expansion can go on forever.

 

[Ibix]

Am I understanding right? If the density of dark energy is non-zero the expansion accelerates. If it's non-zero and constant or decreasing then the "negative pressure" is constant or decreasing and unbound systems separate but bound systems are never destroyed. If it's non-zero and increasing, however, the negative pressure increases and then eventually even bound systems are destroyed.

 

[PeterDonis]

Am I understanding right?

Not quite.

The term "dark energy" means $p = - \rho$, i.e., pressure is minus energy density. This is what a cosmological constant gives you when put in perfect fluid terms. (I'm assuming throughout that $\rho > 0$.)

Accelerated expansion happens for any pressure within the range $- \rho \le p < - \frac{1}{3} \rho$.

The term for $p < - \rho$, which is what you need for a big rip, is "phantom energy".

Some sources use the general form $p = w \rho$, and then dark energy is $w = -1$, accelerated expansion happens for $-1 \le w < - \frac{1}{3}$, and phantom energy/big rip is $w < -1$.

Note that none of this has anything to do with how, or whether, $\rho$ changes with time. That's a separate question, which is relevant if you're trying to figure out what the stuff is actually made of, and for the quantitative details of the dynamics (exactly how fast the expansion accelerates, or how long it takes for the big rip to happen if there is a big rip), but not for the overall qualitative dynamics.

 

[A Middle Aged Man]

If dark energy is actually INCREASING, though, would that point to a continued increase and then finally overwhelming the universe in a big rip?

 

[PeterDonis]

If dark energy is actually INCREASING, though, would that point to a continued increase and then finally overwhelming the universe in a big rip?

I already addressed that in post #6.

 

[A Middle Aged Man]

I hate to say "could you simplify it for me", but...

 

[Ibix]

Not quite.

Very polite - thank you Peter.

So in a $-1\leq w <-1/3$ situation accelerating expansion happens. But co-moving observers who are a finite distance apart at some time are also a finite distance apart at all finite times. Loose analogy - if I start at rest next to you on a Euclidean plane and run away from you with some acceleration $a=Jt$ ($J$ is a positive constant, so my acceleration is increasing) then my distance from you is $Jt^3/6$, which is always finite despite my ever-increasing acceleration.

But a $w<-1$ situation does something nasty to the Friedmann equations so that even bound objects like galaxies are destroyed at finite times, which is very different from the other situation where galaxies separate but do not get destroyed?

 

[timmdeeg]

If I understand it correctly the $w<−1$ situation (big rip) means that tidal forces which are pulling things apart from each other are increasing without bound so that everything gets destroyed.

 

[MikeeMiracle]

A Middle Aged Man: The space between stella objects not bound by common gravity (co-moving) is expanding. So things like galaxy clusters have enough gravity to stay together and counter the effect of any expansion. Think of empty space as expanding, not everything expanding.

If it's just empty space which expands then it points to "The Big Freeze" / "The Big Chill" scenario.

If everything was expanding everywhere then that would lead to "The Big Rip" scenario.

All the evidence is poiting to The Big Freeze scenario at the moment, not The Big Rip. The Big Rip is far more dramatic and makes for great popular science video's which is why it recieve's so much coverage in places like YouTube.

 

[PeterDonis]

So in a ##-1 \le w < - 1/3 situation accelerating expansion happens. But co-moving observers who are a finite distance apart at some time are also a finite distance apart at all finite times.

Yes.

But a $w < −1$ situation does something nasty to the Friedmann equations so that even bound objects like galaxies are destroyed at finite times, which is very different from the other situation where galaxies separate but do not get destroyed?

Not only are bound objects destroyed at finite times for $w < -1$, but any two comoving objects go to infinite separation at a finite time. That's what the big rip is.

 

[Ibix]

Not only are bound objects destroyed at finite times for $w < -1$, but any two comoving objects go to infinite separation at a finite time. That's what the big rip is.

Ah - so in a phantom energy universe you can posit two comoving observers who are less than an atom's width apart and their separation must increase arbitrarily quickly just before the rip singularity, so the atom can't possibly be bound tight enough. But that doesn't occur in a dark energy universe because you never get to infinitely rapid growth of the distance in that way. ...right?

 

[PeterDonis]

that doesn't occur in a dark energy universe because you never get to infinitely rapid growth of the distance in that way. ...right?

Yes.

 

[Ibix]

So - paraphrasing for the benefit of @A Middle Aged Man, in a dark energy universe the distance between unbound objects (like us and a distant galaxy) grows. But because of the way the curvature of spacetime evolves it never starts pulling bound objects (like your body or the galaxy) apart. However, in a phantom energy universe you get a situation at a finite time where the expansion must pull apart bound objects. Both models feature increasing acceleration at large scales, but only the phantom energy model leads to infinitely rapid expansion even between arbitrarily close together points at finite time - the Big Rip. The underlying reason is that dark energy and phantom energy have different properties (specifically, different ranges of ratios between the pressure they exert and their densities), and there's relatively little you can say beyond that without going into details of maths.

I think.

 

[PeterDonis]

in a dark energy universe the distance between unbound objects (like us and a distant galaxy) grows

This is also true of an expanding universe without dark energy. The difference when dark energy is present is that the proper distance between unbound comoving objects grows at a rate that increases with time. (Even this statement has some caveats; you have to be careful how you define the "rate" of growth.)

 

[PAllen]

My understanding is that with any accelerated growth of scale factor, there is, in the limit of perfect fluid, a a tendency of initially parallel (not comoving) geodesics to separate. This produces a very tiny expansion tidal force on bound systems, too small to measure, in practice, but predicted per theory. Similarly, if the second derivative of the scale factor is negative (even if the first derivative remains always positive), there is a tiny compressive tidal force.

 

[PeterDonis]

This produces a very tiny expansion tidal force on bound systems,

Yes, but this force in itself does not eventually break up bound systems; it simply changes slightly the bound states those systems are in. For a given size of a bound system, with ordinary accelerated expansion (i.e., $-1 \le w < - 1/3$), this tidal force is constant in time. (More precisely, it is proportional to the energy density, with a negative proportionality constant, so it can change with time if the energy density changes, but the change is linear in the density.)

What eventually breaks up bound systems if phantom energy is present (i.e., in a big rip scenario) is that the "expansion tidal force" increases without bound in finite time even if the energy density is constant.

 

[timmdeeg]

What eventually breaks up bound systems if phantom energy is present (i.e., in a big rip scenario) is that the "expansion tidal force" increases without bound in finite time even if the energy density is constant.

Ah, thanks for conforming post #11.