On covariant perturbations with scalar field in modified Gauss-Bonnet gravity

TL;DR

This paper studies how cosmological perturbations evolve in modified Gauss-Bonnet gravity with a scalar field, revealing differences from standard Lambda CDM and providing numerical solutions for specific models.

Contribution

It presents a covariant formalism for perturbations in f(G) gravity with scalar fields and derives fully perturbed equations in redshift space, including numerical analysis.

Findings

Energy overdensity perturbations decay with redshift.

Perturbations differ significantly from Lambda CDM in certain f(G) models.

Results reduce to GR when f(G) approaches G and scalar field is absent.

Abstract

We investigate cosmological perturbations of f(G) gravity in the presence of a scalar field. Using the 1 + 3 covariant formalism, we present the energy overdensity perturbation equations responsible for large scale structure formation. After applying harmonic decomposition method together with the redshift transformation technique, we obtain the fully perturbed equations in redshift space. The equations are solved to study the growth of matter overdensities contrast with redshift. For both short- and long-wavelength modes, we obtain numerical results for particular functional form f(G) models and scalar field. We find that, for this choice the energy overdensity perturbations decay with increase in redshift. However, for both short- and long- wavelength modes, the perturbations which include amplitude effects due to the f(G) models with a scalar field do differ remarkably from those in Lambda CDM. The results reduce to GR results in the limit of f(G) tends to G and in the absence of scalar field.