On 1 + 3 covariant perturbations of the quasi-Newtonian spacetime in modified Gauss–Bonnet gravity

Abstract

The consideration of a [Formula: see text] covariant approach to cold dark matter universe with no shear cosmological dust model with irrotational flows is developed in the context of [Formula: see text] gravity theory in this study. This approach reveals the existence of integrability conditions which do not appear in noncovariant treatments. We constructed the integrability conditions in modified Gauss–Bonnet [Formula: see text] gravity basing on the constraints and propagation equations. These integrability conditions reveal the linearized silent nature of quasi-Newtonian models in [Formula: see text] gravity. Finally, the linear equations for the overdensity and velocity perturbations of the quasi-Newtonian spacetime were constructed in the context of modified [Formula: see text] gravity. The application of harmonic decomposition and redshift transformation techniques to explore the behavior of the overdensity and velocity perturbations using [Formula: see text] model was made. On the other hand, we applied the quasi-static approximation to study the approximated solutions on small scales which helps to get both analytical and numerical results of the perturbation equations. The analysis of the energy overdensity and velocity perturbations for both short- and long-wavelength modes in a dust-Gauss–Bonnet fluids was done and we see that both energy overdensity and velocity perturbations decay with redshift for both modes. In the limits to [Formula: see text]CDM, it means [Formula: see text] the considered [Formula: see text] model results coincide with [Formula: see text]CDM.