How Does Delta_k Transform in a Uniformly Moving Frame in Fourier Space?

[cosmoboy]

can somebody help me to find an expression for the density contrast
(in fouruer space; delta_k) in a moving frame. Basically I am trying to
figure out how various quantities like power spectrum P(k) etc., will look in a uniformly moving frame .

 

[hellfire]

I would say you need to consider the relativistic perturbation theory on a Robertson-Walker spacetime (this is described in chapter 10, p. 275 to 280 of "Principles of Physical Cosmology", Peebles) and then you need to perform a coordinate transformation. But I have no clue how to proceed with this second step, because it seams to me that the usual approximations which can be done for perturbation theory in Minkowski space (background Lorentz transformation as described in chapter 8 of "A first course in general relativity", Schutz) are not valid due to the expansion of space. So probably I have not tell you anything new, but I would be also interested in the answer to this question. Have you any idea how to proceed?

 

[cosmoboy]

delta_k

In Peebles physical cosmology nothing of that sort is dicussed on that page; I am basically interested in Fourier space. I have found this discussion at two places.
1. In Peebles "The large scale structure of the Universe" in chapter 11 page 134; on top of this page it is discussed how to go in the center of mass frame.

2. There is some discussion of this type on page 210 of http://arxiv.org/abs/astro-ph/0112551

Basic problem is: if x -----> x' = x + dx , we have to find:
delta_k -----> ? ; note : point is that for finding delta_k ; x is integrated out. I am wondering will delta_k change at all ?