Cosmological perturbations and quasistatic assumption in f(R) theories

Mu-Chen Chiu, Andy Taylor, Chenggang Shu, and Hong Tu
Phys. Rev. D 92, 103514 – Published 18 November 2015

Abstract

f(R) gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach (a combination of the quasistatic approximation and sub-Hubble limit) for cosmic perturbations is good enough to describe the evolution of large scale structure in f(R) models, some studies have suggested that this method is not valid for all f(R) models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, Ψ, and the curvature potential, Φ. Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that the Compton length controls the quasistatic behaviors in f(R) gravity. In addition, regardless the validity of quasistatic approximation, a strong version of the sub-Hubble limit alone is sufficient to reduce the exact linear perturbations in any viable f(R) gravity to second order. Our findings disagree with some previous studies where we find little difference between our exact and quasi-Newtonian solutions even up to k=10c1H0.

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  • Received 13 May 2015

DOI:https://doi.org/10.1103/PhysRevD.92.103514

© 2015 American Physical Society

Authors & Affiliations

Mu-Chen Chiu1,2,*, Andy Taylor1,†, Chenggang Shu2, and Hong Tu2

  • 1Scottish University Physics Alliance, Institute for Astronomy, The Royal Observatory, University of Edinburgh, Blackford Hill, Edinburgh EH9 3HJ, United Kingdom
  • 2Shanghai Key Lab for Astrophysics, Shanghai Normal University, Shanghai 200234, China

  • *chiumuchen@gmail.com
  • ant@roe.ac.uk

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Vol. 92, Iss. 10 — 15 November 2015

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