Gravitational waves in cosmology?

[TEFLing]

The usual calculations for gravitational waves linearize the GR equations around the background solution of flat space time ( g = Minkowski metric matrix ) empty of matter and energy ( T = 0 )

What happens in cosmology, when one must linearize the GR equations about the FRW metric matrix with cosmological constant ( on the LHS ) and uniform energy density and pressure ( on the RHS ) ?

Intuitively, the presence of matter throughout the fabric of space time would damp out gravitational waves... The matter could absorb some of the wave energy, like coins carpeting the often mentioned trampoline / rubber sheet. And what about the effects of the cosmological constant... Considered as an intrinsic tendency for curvature of the fabric of space time, maybe it amplifies gravitational waves??

Has anyone linearized the GR equations around the FRW + cc metric / uniform universe SET solution? Any popular or journal articles perhaps or other derivations? Seems like the cosmological background solution would have some interesting and perhaps important differences from the flat empty space solution

 

[phinds]

Intuitively, the presence of matter throughout the fabric of space time would damp out gravitational waves...

No more than it damps out light and we still have no trouble seeing galaxies some 13Billion LY away.

And what about the effects of the cosmological constant

"red shift" (in the sense of lowering the frequency) exactly as with light.

 

[TEFLing]

No more than it damps out light and we still have no trouble seeing galaxies some 13Billion LY away.

"red shift" (in the sense of lowering the frequency) exactly as with light.

First I never said the effect would be strong but matter does impede the propagation of light slightly, yes?
Also the cosmological constant contributes to but doesn't CAUSE redshift yes?

 

[phinds]

First I never said the effect would be strong but matter does impede the propagation of light slightly, yes?

To an insignificant degree, sure, but it doesn't slow down the wave that do reach us (assuming there are such things as gravitational waves, which does seem likely even thought they haven't been detected yet)

Also the cosmological constant contributes to but doesn't CAUSE redshift yes?

If the cosmological constant is in fact "dark energy" then yes, it causes red shift (along with normal expansion, but it's mostly due to the acceleration, I think)

 

[PeterDonis]

If the cosmological constant is in fact "dark energy" then yes, it causes red shift (along with normal expansion, but it's mostly due to the acceleration, I think)

Not really. The best way to think of the redshift is as a measure of how much larger the universe is at the time of reception, compared to the time of emission. Mathematically, this relative expansion factor is $1 + z$, where $z$ is the redshift. So $1 + z = 2$ means the universe is twice as large when you receive the light as it was when the light was emitted. (If thinking of the universe as having a "size" is problematic for you, since as far as we can tell it's spatially infinite, just substitute "scale factor" for "size of the universe".)

You can't really separate out "normal expansion" from "acceleration" when you look at it this way; both of them contribute, and it's not clear how to quantify "how much" each contributes. What's important is the total effect.

 

[phinds]

OK, I guess where I must be going wrong is that I thought that without the acceleration the expansion would not be producing nearly as much redshift as it is because the recession velocity would not be as high as it is (within the observable universe)

 

[PeterDonis]

without the acceleration the expansion would not be producing nearly as much redshift as it is

You're looking at it backwards. When I look at an object with a given redshift, I already know how much the universe has expanded between the object emitting the light and my seeing it--that's what the redshift tells me. What the redshift doesn't tell me is how long it took for the universe to expand by that factor--i.e., how long ago the light was emitted. That's what depends on the specifics of the dynamics--whether the dominant energy density is radiation, matter, or dark energy. So the variable is not really "how much expansion is produced" but "how long does it take to produce a given amount of expansion". But again, you can't really quantify individual effects of the different kinds of energy density on this; what's important is the total effect.

 

[phinds]

Interesting. Thanks.