Cosmological Perturbations In F (G) Gravity

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 analyze energy-density perturbations for two fluid systems, namely, for a Gauss-Bonnet field-dust system and for a Gauss-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.