Why is there no consensus on the big rip?

[zeromodz]

We all know that the Hubble equations tell us that in a vacuum dominated universe, that the scale factor will expand exponentially.

H^2 = (da/dt)^2 * 1/a^2
Ha = da/dt
a = e^(Ht)

Where proper distance is

d = aΔx
v = Hd
v = HaΔx <- The velocity between any two points in space is proportional to a soon to be infinite scale factor.

Where x is just coordinate convention. In a vacuum dominated universe, H is constant due to the vacuum density being constant. As a t approaches infinity, so does the scale factor (a). Therefore, in the far distant future our universe will exponentially grow to infinity no matter the coordinate distance, since proper distance is proportional the scale factor. Does this not mathematically prove that the big rip is true?

 

[marcus]

We all know that the Hubble equations tell us that in a vacuum dominated universe, that the scale factor will expand exponentially.

H^2 = (da/dt)^2 * 1/a^2
Ha = da/dt
a = e^(Ht)

Where proper distance is

d = aΔx
v = Hd
v = HaΔx <- The velocity between any two points in space is proportional to a soon to be infinite scale factor.

Where x is just coordinate convention. In a vacuum dominated universe, H is constant due to the vacuum density being constant. As a t approaches infinity, so does the scale factor (a). Therefore, in the far distant future our universe will exponentially grow to infinity no matter the coordinate distance, since proper distance is proportional the scale factor. Does this not mathematically prove that the big rip is true?

It does not mathematicall prove that "big rip" as normally understood is true.

It just proves what you showed, exponential expansion. The Hubble parameter will continue to decline but the decline will level out to a constant, in the limit we have a deSitter model which is certainly NOT big rip.

deSitter U has constant H, and exponential growth of distance.

According to the standard LCDM model with current dark energy fraction 0.73 and Hubble parameter 71 (km/s per Mpc) the asymptotic value of H will be sqrt(0.73)*71 which is about 61 km/s per Mpc.

The current H = 71 translates into about 1/140 percent increase in distance every 1 million years.

The asymptotic rate will be about 1/160 of one percent distance growth every 1 million years. No galaxies will be pulled apart. So not to worry

So far there is no obs. evidence that dark energy is acting big rippish. Evidence is consistent with it being a peaceful cosmological constant. In that case accelerated expansion leads to declining H going to a constant, like 61, in the limit. You have to understand that accelerated growth of the scale factor a(t) does NOT imply that H increases. Ask questions if you have any trouble understanding that.

 

[bcrowell]

It depends on the properties of dark energy, which can be characterized by $w=p/\rho$. The default assumption is that dark energy is a cosmological constant, which means w=-1. In that case, the scale factor increases exponentially, as you've said.

But a bound system like the solar system does not simply expand according to the scale factor, with a velocity proportional to $\dot{a}/a$. The strain on an object due to cosmological expansion is proportional to $\ddot{a}/a$. See Cooperstock, http://arxiv.org/abs/astro-ph/9803097v1 . This strain is currently many orders of magnitude too small to have any observable effect on our solar system, for example. The idea here is that even in flat spacetime, you can get $\dot{a}/a\ne 0$ just by a change of coordinates, so it can't have any dynamical effect on a bound system. Only the second derivative produces an effect, and the second derivative is currently very small.

For w=-1, which gives exponential expansion, $\ddot{a}/a$ is constant, so the strain will never be any bigger than it is now. You only get a big rip for w<-1.

I think the original paper on this is Caldwell et al., "Phantom Energy and Cosmic Doomsday," http://arxiv.org/abs/astro-ph/0302506

 

[edgepflow]

The cosmological constant that could lead to the big rip may not be constant. See Section 5.2 of

http://arxiv.org/abs/astro-ph/0009491

This is one of my favorite papers. Most of it is written simply enough that even I can understand it.

There are three possibilities from this paper:

a) The scalar field is is at a true minimum and the cosmological constant is constant. This may (or may not as others discussed) end up in a big rip.

b) Universe is in a metastable false vacuum state - subject to tunneling (and no big rip).

c) scaler field of universe is slow rolling down - again no big rip.

 

[zeromodz]

It does not mathematicall prove that "big rip" as normally understood is true.

It just proves what you showed, exponential expansion. The Hubble parameter will continue to decline but the decline will level out to a constant, in the limit we have a deSitter model which is certainly NOT big rip.

deSitter U has constant H, and exponential growth of distance.

According to the standard LCDM model with current dark energy fraction 0.73 and Hubble parameter 71 (km/s per Mpc) the asymptotic value of H will be sqrt(0.73)*71 which is about 61 km/s per Mpc.

The current H = 71 translates into about 1/140 percent increase in distance every 1 million years.

The asymptotic rate will be about 1/160 of one percent distance growth every 1 million years. No galaxies will be pulled apart. So not to worry

So far there is no obs. evidence that dark energy is acting big rippish. Evidence is consistent with it being a peaceful cosmological constant. In that case accelerated expansion leads to declining H going to a constant, like 61, in the limit. You have to understand that accelerated growth of the scale factor a(t) does NOT imply that H increases. Ask questions if you have any trouble understanding that.

1)What logic do you use by taking the square root of the dark energy fraction and multiplying it times the Hubble parameter to find its asymptotic value?

2)I thought the scale factor was what determined how fast things moved from each other? All you need to do is plug in the scale factor to the distance like I already did and you will find that the expansion velocity is proportional to the Hubble parameter (Which I set constant for simplicity) and the scale factor.

V = Ha(t)X

 

[Chalnoth]

The big rip is not exponential expansion. With exponential expansion, there is a constant cosmological horizon. In a big rip, the cosmological horizon shrinks with time, with the Hubble parameter increasing in time. This is highly, highly unlikely to be possible.

 

[marcus]

1)What logic do you use by taking the square root of the dark energy fraction and multiplying it times the Hubble parameter to find its asymptotic value?

2)I thought the scale factor was what determined how fast things moved from each other? All you need to do is plug in the scale factor to the distance like I already did and you will find that the expansion velocity is proportional to the Hubble parameter (Which I set constant for simplicity) and the scale factor.

V = Ha(t)X

1) My logic is just the basic equation of cosmology---the Friedmann equation. Have a look at the equation (a simplified form of the Einst. Eqn.). It governs the H = a'/a
and it shows that if the cosmo constant (dark energy density) stays constant then there is only one thing that H can tend to. Just simple math.

2) By definition H = a'/a. It is the PERCENTAGE or fractional rate that distances increase. Largescale distances, not distances between bound stuff like.

You can work it out: H is currently the fractional expansion rate of approx. 1/140 of one percent every million years. It is simply converting some units. Google calculator, for example, will do it for you.
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Your problem is understanding how exponential growth can be very slow percentage wise.
By the time some distance is expanding fast, like several times faster than light, if is already very big. Little distances don't need to expand fast, in exponential growth. They only expand fast much later when they have grown huge. So exponential growth does not lead to a big rip picture.

It is like putting a small amount of money in the bank to get 2% interest. It does not increase very fast. It only would increase fast after a long time when it gets big.
==========================

Your title of the thread is a bit peculiar. AFAICS there is a lot of consensus. So it does not seem to make sense to as why there is "no consensus". everybody here is telling you the same thing---essentially that you need to understand exponential growth at a near constant small percentage rate better.

Near constant exponential growth is what we have, what we see by observation. of the late universe. Like Chalnoth says: expo'l growth is not "big rip". In big rip even small distances increase fast.
I should shut up and let Chalnoth say this. Or Ben Crowell. Good luck understanding what they are telling!

 

[bcrowell]

This is highly, highly unlikely to be possible.

I don't know how to assign a probability to w<-1. As far as I know there is no consensus either for or against a big rip. As the WP article states, the observational constraints simply aren't strong enough to say anything either way.

It's true that w<-1 violates the dominant energy condition (DEC), while w=-1 is at the edge of the DEC and only violates stronger energy conditions like the strong energy condition (SEC). But there is no clear reason to believe that the DEC must always hold while the SEC needn't: http://arxiv.org/abs/gr-qc/0205066

 

[Aimless]

A "Big Rip" is a future singularity in which, at a finite time, the scale factor, the energy density, and the pressure all become pathological. By investigating the Friedmann equation, one can easily show that none of these is true for de Sitter space.

Nojiri et. al. presented a classification scheme for types of future singularities: http://arxiv.org/abs/hep-th/0501025

 

[Chalnoth]

I don't know how to assign a probability to w<-1. As far as I know there is no consensus either for or against a big rip. As the WP article states, the observational constraints simply aren't strong enough to say anything either way.

It's true that w<-1 violates the dominant energy condition (DEC), while w=-1 is at the edge of the DEC and only violates stronger energy conditions like the strong energy condition (SEC). But there is no clear reason to believe that the DEC must always hold while the SEC needn't: http://arxiv.org/abs/gr-qc/0205066

The possibility of w < -1 wasn't even considered in observational results until some theorists came up with models that allowed for measurements of w < -1 without a big rip (basically, you can do this by having interactions between matter and dark energy that make it so that matter doesn't scale as 1/a^3, which causes us to misunderstand the scaling of dark energy).

The main reason why real w < -1 isn't considered seriously is that it violates the weak energy condition of General Relativity, which states that the matter density is always positive for any observer.

 

[bcrowell]

The main reason why real w < -1 isn't considered seriously is that it violates the weak energy condition of General Relativity, which states that the matter density is always positive for any observer.

I haven't seen any evidence that it "isn't considered seriously." Do you have any evidence for this claim from reliable sources such as peer-reviewed journals?

Yes, it violates certain energy conditions. As I pointed out in #8, a cosmological constant also violates various energy conditions. As I also pointed out in #8, there is no clear reason to believe that some energy conditions absolutely must be true even though others have turned out to be false. In fact, as discussed in the reference I gave in #8 to a paper published in a peer-reviewed journal, there are fundamental reasons to believe that all energy conditions, including the WEC, are violated under certain circumstances. For example, the Casimir effect can violate both the WEC and the averaged WEC.

 

[Chalnoth]

I haven't seen any evidence that it "isn't considered seriously." Do you have any evidence for this claim from reliable sources such as peer-reviewed journals?

Yes, it violates certain energy conditions. As I pointed out in #8, a cosmological constant also violates various energy conditions. As I also pointed out in #8, there is no clear reason to believe that some energy conditions absolutely must be true even though others have turned out to be false. In fact, as discussed in the reference I gave in #8 to a paper published in a peer-reviewed journal, there are fundamental reasons to believe that all energy conditions, including the WEC, are violated under certain circumstances. For example, the Casimir effect can violate both the WEC and the averaged WEC.

Violation of this energy condition causes an unstable vacuum. It looks like I might have been mistaken, however. It looks like it is the dominant energy condition which must be broken (though the dominant energy condition requires the weak energy condition). The dominant energy condition states that no matter density travels faster than light.

Anyway, you can get around this through various very roundabout means, but they tend to produce extremely contrived theories, usually with w < -1 being temporary. See here for example:
http://arxiv.org/abs/astro-ph/0301273

 

[bapowell]

What about effective theories that give $w<-1$?

 

[Chalnoth]

What about effective theories that give $w<-1$?

I believe that paper I linked discusses one such idea. As I mentioned, such proposals tend to be highly contrived and seemingly unlikely. They furthermore don't necessarily lead to a rip, as they tend to only have w < -1 temporarily.