Redshift-space distortion in modified Gauss–Bonnet gravity

In the present paper, we consider both background dynamic and cosmological perturbations in the framework of modified Gauss–Bonnet gravity model (i.e. f ( G )) which is effective in fitting observational datasets. We assume a specific functional form of it as f(G)=α Gⁿ f ( G ) = α G n , where α α and n are model parameters. After studying the predictions on the expansion history as revealed by CC, CMB, BAO-DESI, Pantheon+SH0ES and Union 3.0 datasets, a suitable constraining of the cosmological parameters has been opted for. We show the linear cosmological perturbations for the full system to investigate the matter fluctuations under the covariant technique. The solutions to the coupled system of perturbation equations are then computed both in long- and short-wavelength modes, in a dust-Gauss–Bonnet fluids system. Using the redshift-space distortion (RSD) datasets consisting of fσ ₈ f σ 8 values and MCMC simulations, we present the best-fit cosmological parameters (viz. H₀ H 0 , Ω ₘ₀ Ω m 0 , σ ₈ σ 8 and n ).