Difference between Dark Energy and Cosmological Constant

**bombadil** · Sep22-09, 11:30 PM

Can someone remind me what the difference between the Cosmological Constant ( $LaTeX Code: \\Lambda$ ) and Dark Energy (DE)? Doesn't DE (with w = -1) show up in the Einstein's field equations in exactly the same way as $LaTeX Code: \\Lambda$ does?

(In case your an expert, I was trying to understand the conclusion of this paper)

**Chalnoth** · Sep23-09, 02:50 AM

Originally Posted by bombadil

Can someone remind me what the difference between the Cosmological Constant ( $LaTeX Code: \\Lambda$ ) and Dark Energy (DE)? Doesn't DE (with w = -1) show up in the Einstein's field equations in exactly the same way as $LaTeX Code: \\Lambda$ does?

(In case your an expert, I was trying to understand the conclusion of this paper)

"Dark Energy" basically means the (currently unknown) cause of the observed accelerated expansion. The cosmological constant is a specific proposal for what dark energy might be.

Dark energy with w = -1 is considered to be the exact same thing as the cosmological constant.

What they're saying in the conclusion there is that there's a tentative signal that may indicate that the correct explanation for the accelerated expansion may be modified gravity, as opposed to something like the cosmological constant or a scalar field.

**bombadil** · Sep23-09, 09:22 AM

Originally Posted by Chalnoth

What they're saying in the conclusion there is that there's a tentative signal that may indicate that the correct explanation for the accelerated expansion may be modified gravity, as opposed to something like the cosmological constant or a scalar field.

I don't think the author is claiming a detection of modified gravity. In the conclusion she says, "The COSMOS data gives the first signal that dark energy might be a modification to GR, rather than $LaTeX Code: \\Lambda$ ." I'm guessing she's saying that the equation of state parameter, w, evolves with redshift, which is inconsistent with $LaTeX Code: \\Lambda$ .

**Chalnoth** · Sep23-09, 09:28 AM

Originally Posted by bombadil

I don't think the author is claiming a detection of modified gravity. In the conclusion she says, "The COSMOS data gives the first signal that dark energy might be a modification to GR, rather than $LaTeX Code: \\Lambda$ ." I'm guessing she's saying that the equation of state parameter, w, evolves with redshift, which is inconsistent with $LaTeX Code: \\Lambda$ .

No, she's using a different parameterization of gravity itself, not of some matter/energy with w different than -1. Weak lensing constrains possible deviations from General Relativity by carefully tracing the growth of structure, as there are specific relations that GR must follow, whether or not there is some form of matter out there with w < -1/3 (w < -1/3 is required to explain the observed acceleration).

**Wallace** · Sep23-09, 09:54 AM

Originally Posted by Chalnoth

No, she's using a different parameterization of gravity itself, not of some matter/energy with w different than -1. Weak lensing constrains possible deviations from General Relativity by carefully tracing the growth of structure, as there are specific relations that GR must follow, whether or not there is some form of matter out there with w < -1/3 (w < -1/3 is required to explain the observed acceleration).

Exactly right. There are relationships that must hold between the distance history and structure formation if GR is correct. This study is probing those relationships, not w itself as such.

There is a slight problem that some people use the term 'dark energy' to mean 'all models than can be described by some function w(a) within GR' while others use it more broadly to mean 'whatever is causing the apparent acceleration'. The author is this paper is clearly using the latter definition when saying "The COSMOS data gives the first signal that dark energy might be a modification to GR, rather than $LaTeX Code: \\Lambda$ ".

It is a very interesting paper that is sure to provoke similiar studies with other data sets, but I suspect there won't be many people convienced by the results just yet.

**bombadil** · Sep24-09, 01:07 PM

Oops, you both are totally correct, thanks for the help. This looks like an exciting way of investigating the cosmological constant vs modified GR. What would you guess is the largest cause of error? Photometric redshifts used for weak lensing? Or is the statistical analysis itself really tricky?

**Chalnoth** · Sep24-09, 04:12 PM

Originally Posted by bombadil

Oops, you both are totally correct, thanks for the help. This looks like an exciting way of investigating the cosmological constant vs modified GR. What would you guess is the largest cause of error? Photometric redshifts used for weak lensing? Or is the statistical analysis itself really tricky?

Photometric redshifts can have catastrophic errors (e.g. you can classify a z=1 galaxy as a z=4 galaxy, and vice versa), and so those need to be quantified. There's also problems with galaxy bias: we don't understand galaxies all that well, nor do we understand all that well how galaxies trace matter. So that's a difficulty that needs to be managed. Another problem is that interacting galaxies can "simulate" a weak lensing signal, because their axes will tend to be aligned (weak lensing analyses generally assume that galaxies are intrinsically uncorrelated).

These are all manageable, of course, but there is a fair amount of difficulty in doing it right. I didn't look closely at the paper, but as a single-author paper, my initial response would be to be a bit skeptical that it was all done well enough (just because it requires a good amount of work to do so). However, not having really read it, I can't actually place any judgment here, and it's a bit outside my area of expertise anyway, so I would trust my own evaluation too much even if I did read it in detail.