Cosmological perturbations in f(G) gravity

Abstract

We explore cosmological perturbations in a modified Gauss-Bonnet f(G) gravity, using a 1+3 covariant formalism. In such a formalism, we define gradient variables to get perturbed linear evolution equations. We transform these linear evolution equations into ordinary differential equations using a spherical harmonic decomposition method. The obtained ordinary differential equations are time-dependent and then transformed into redshift dependent. After these transformations, we analyse energy-density perturbations for two fluid systems, namely for a Gauss-Bonnet field-dust system and for a Gaus-Bonnet field-radiation system for three different pedagogical f(G) models: trigonometric, exponential and logarithmic. For the Gauss-Bonnet field-dust system, energy-density perturbations decay with increase in redshift for all the three models. For the Gauss-Bonnet field-radiation system, the energy-density perturbations decay with increase in redshift for all of the three f(G) models for long wavelength modes whereas for short wavelength modes, the energy-density perturbations decay with increasing redshift for the logarithmic and exponential f(G) models and oscillate with decreasing amplitude for the trigonometric f(G) model