  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
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 an increase in redshift for all
three models. For the Gauss-Bonnet field-radiation system, the energy-density
perturbations decay with an 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.
