Cosmological perturbations in f(G) gravity

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