## [0808.0003] Testing cosmological structure formation using redshift-space distortions

 Authors: Will J Percival, Martin White Abstract: Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for observing the build-up of cosmological structure. In this paper we develop and test a new statistic based on anisotropies in the measured galaxy power spectrum, which is independent of galaxy bias and matches the matter power spectrum shape on large scales. The amplitude provides a constraint on the derivative of the linear growth rate through f.sigma_8. This demonstrates that spectroscopic galaxy surveys offer many of the same advantages as weak lensing surveys, in that they both use galaxies as test particles to probe all matter in the Universe. They are complementary as redshift-space distortions probe non-relativistic velocities and therefore the temporal metric perturbations, while weak lensing tests the sum of the temporal and spatial metric perturbations. The degree to which our estimator can be pushed into the non-linear regime is considered and we show that a simple Gaussian damping model, similar to that previously used to model the behaviour of the power spectrum on very small scales, can also model the quasi-linear behaviour of our estimator. This enhances the information that can be extracted from surveys for LCDM models. [PDF]  [PS]  [BibTex]  [Bookmark]

Discussion related to specific recent arXiv papers
Sarah Bridle
Posts: 144
Joined: September 24 2004
Affiliation: University College London (UCL)
Contact:

### [0808.0003] Testing cosmological structure formation using

This seems like a really neat result.

Apparently the old way of writing redshift space distortions (Kaiser formula - eqn 10 in this paper) was a good way to write down the redshift space power spectrum compactly. But it makes it look like the only thing you can measure from redshift space power spectra is the parameter βΩm0.6 / b, and thus you learn a degenerate combination of cosmology and bias (the 0.6 is replaced by a function of w in dark energy models).

This paper shows that you can actually write things in a different way (e.g. their eqn 12) in which the cosmology and bias parts have different dependencies on the direction in k-space (mu) and thus can be separated.

I think this paper deserves some sort of prize for a very nice result, but also some sort of anti-prize for having the most boring figures ever! We just had a journal club on it at JPL and would have been happy with an even more user-friendly qualitative explanation of the effect, with accompanying figure, e.g. something as a function of mu? and maybe also just show the good old butterfly diagram again? In fact I would still be happy to read a nice paragraph on why this works (no equations).

Finally - the paper makes a bold statement in the abstract, and I am falling for the bait laid out for lensers by quoting it here:
"This places redshift space distortion measurements on the same footing as weak lensing measurements in the sense that they both allow us to test the matter distribution directly."
The qualification in the second half of the sentence is clear, and this paper cannot be expected to do a full analysis of constraints from future surveys. But it will be interesting to see how tight the constraints actually are on the growth rate from future surveys using this method (e.g. as compared to weak lensing).

Niayesh Afshordi
Posts: 49
Joined: December 17 2004
Affiliation: Perimeter Institute/ University of Waterloo
Contact:

### [0808.0003] Testing cosmological structure formation using r

Predictions for future measurements of fσ8 from redshift distortions (as well as current constraints) can be found in Fig.2 of 0807.0810.

Douglas Clowe
Posts: 11
Joined: November 05 2005
Affiliation: Ohio University

### [0808.0003]

Am I correct in reading this paper that their strongest constraints depend on the assumption that the bias is linear? Once that breaks down, they have the relations depend on functions of $k$ and $\mu^2$, but only have limits for those functions.