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[0808.0003]
Testing cosmological structure formation using redshiftspace distortions

Authors:  Will J Percival, Martin White 
Abstract:  Observations of redshiftspace distortions in spectroscopic galaxy surveys
offer an attractive method for observing the buildup 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 redshiftspace distortions probe nonrelativistic 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 nonlinear 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
quasilinear behaviour of our estimator. This enhances the information that can
be extracted from surveys for LCDM models. 

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Sarah Bridle
Joined: 24 Sep 2004 Posts: 149 Affiliation: University College London (UCL)

Posted: August 13 2008 


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 β ≈ Ω_{m}^{0.6} / 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 kspace (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 antiprize 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 userfriendly 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). 

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Niayesh Afshordi
Joined: 17 Dec 2004 Posts: 62 Affiliation: Perimeter Institute/ University of Waterloo

Posted: August 13 2008 


Predictions for future measurements of fσ_{8} from redshift distortions (as well as current constraints) can be found in Fig.2 of 0807.0810. 

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Douglas Clowe
Joined: 05 Nov 2005 Posts: 12 Affiliation: Ohio University

Posted: August 19 2008 


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 μ^{2}, but only have limits for those functions. 

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