Going beyond the Kaiser redshift-space distortion formula: A full general relativistic account of the effects and their detectability in galaxy clustering

Jaiyul Yoo, Nico Hamaus, Uroš Seljak, and Matias Zaldarriaga
Phys. Rev. D 86, 063514 – Published 17 September 2012

Abstract

Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing to velocity effect. We perform a Fisher matrix analysis of detectability of these terms and show that in a single tracer survey they are completely undetectable. To detect these terms one must resort to the recently developed methods to reduce sampling variance and shot noise. We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M1012h1M (this can increase to 10σ or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect primordial non-Gaussianity is little compromised.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 25 June 2012

DOI:https://doi.org/10.1103/PhysRevD.86.063514

© 2012 American Physical Society

Authors & Affiliations

Jaiyul Yoo1,2,*, Nico Hamaus1, Uroš Seljak1,2,3,4, and Matias Zaldarriaga5

  • 1Institute for Theoretical Physics, University of Zürich, CH-8057 Zürich, Switzerland
  • 2Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, USA
  • 3Physics Department and Astronomy Department, University of California, Berkeley, California 94720, USA
  • 4Institute for the Early Universe, Ewha Womans University, 120-750 Seoul, South Korea
  • 5School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA

  • *jyoo@physik.uzh.ch

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 86, Iss. 6 — 15 September 2012

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×