Cosmology of modified Gauss-Bonnet gravity

Baojiu Li, John D. Barrow, and David F. Mota
Phys. Rev. D 76, 044027 – Published 30 August 2007

Abstract

We consider the cosmology where some function f(G) of the Gauss-Bonnet term G is added to the gravitational action to account for the late-time accelerating expansion of the universe. The covariant and gauge invariant perturbation equations are derived with a method which could also be applied to general f(R,RabRab,RabcdRabcd) gravitational theories. It is pointed out that, despite their fourth-order character, such f(G) gravity models generally cannot reproduce arbitrary background cosmic evolutions; for example, the standard ΛCDM paradigm with ΩDE=0.76 cannot be realized in f(G) gravity theories unless f is a true cosmological constant because it imposes exclusionary constraints on the form of f(G). We analyze the perturbation equations and find that, as in the f(R) model, the stability of early-time perturbation growth puts some constraints on the functional form of f(G), in this case 2f/G2<0. Furthermore, the stability of small-scale perturbations also requires that f not deviate significantly from a constant. These analyses are illustrated by numerically propagating the perturbation equations with a specific model reproducing a representative ΛCDM cosmic history. Our results show how the f(G) models are highly constrained by cosmological data.

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  • Received 25 May 2007

DOI:https://doi.org/10.1103/PhysRevD.76.044027

©2007 American Physical Society

Authors & Affiliations

Baojiu Li1,*, John D. Barrow1,†, and David F. Mota2,‡

  • 1Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, University of Cambridge, Cambridge CB3 0WA, United Kingdom
  • 2Institute of Theoretical Physics, University of Heidelberg, 69120 Heidelberg, Germany

  • *B.Li@damtp.cam.ac.uk
  • J.D.Barrow@damtp.cam.ac.uk
  • d.mota@thphys.uni-heidelberg.de

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Issue

Vol. 76, Iss. 4 — 15 August 2007

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