Large-scale clustering of galaxies in general relativity

Donghui Jeong, Fabian Schmidt, and Christopher M. Hirata
Phys. Rev. D 85, 023504 – Published 4 January 2012

Abstract

Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we retrace these calculations and show that, on scales approaching the horizon, the observed galaxy power spectrum depends strongly on which gauge is assumed to relate the intrinsic fluctuations in galaxy density to matter perturbations through a linear bias relation. Starting from simple physical assumptions, we derive a gauge-invariant expression relating galaxy density perturbations to matter density perturbations on large scales, and show that it reduces to a linear bias relation in a synchronous-comoving gauge, corroborating an assumption made in several recent papers. We evaluate the resulting observed galaxy power spectrum, and show that it leads to corrections similar to an effective non-Gaussian bias corresponding to a local fNL,eff0.5. This number can serve as a guideline as to which surveys need to take into account relativistic effects. We also discuss the scale-dependent bias induced by primordial non-Gaussianity in the relativistic context, which again is simplest in a synchronous-comoving gauge.

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  • Received 19 August 2011

DOI:https://doi.org/10.1103/PhysRevD.85.023504

© 2012 American Physical Society

Authors & Affiliations

Donghui Jeong1,2, Fabian Schmidt1, and Christopher M. Hirata1

  • 1Theoretical Astrophysics, California Institute of Technology, Mail Code 350-17, Pasadena, California 91125, USA
  • 2Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA

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Issue

Vol. 85, Iss. 2 — 15 January 2012

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