Cosmology in modified $f(\mathcal{G})$ gravity: a late time cosmic phenomena

TL;DR

This paper develops a numerical method to analyze $f( ext{G})$ gravity models, constrains them with cosmic data, and finds they can mimic standard cosmology at low redshift but differ at high redshift, offering an alternative explanation for cosmic acceleration.

Contribution

It introduces a numerical solution approach for $f( ext{G})$ gravity, applies Bayesian analysis with observational data, and performs stability analysis, advancing the understanding of modified gravity models in cosmology.

Findings

$f( ext{G})$ models fit low-redshift data similar to $ ext{Lambda CDM}$.

Significant deviations occur at high redshift, lacking a matter-dominated epoch.

The model can explain current cosmic acceleration and has stable critical points.

Abstract

In this work, we present a method for numerically solving the Friedmann equations of modified $f(\mathcal{G})$ gravity in the presence of pressureless matter. This method enables us to predict the redshift behaviour of the Hubble expansion rate. To evaluate the credibility of the model, we applied a Bayesian MCMC technique using late-time cosmic observations to impose limitations on the free parameters of the Gauss-Bonnet model. Our results suggest that the $f(\mathcal{G})$ model can reproduce the low-redshift behaviour of the standard Lambda cold dark matter ($\Lambda$CDM) model, but there are significant differences at high redshifts, leading to the absence of a standard matter-dominated epoch. We also examined the profiles of cosmographic parameters using the model parameter values from the standard range to verify the intermediate epochs. Our analysis shows that the highly promising $f(\mathcal{G})$ model is a feasible candidate for explaining the current epochs. We presented a dynamical system analysis framework to examine the stability of the model. Our study identified critical points depicting various phases of the Universe and explained the evolutionary epochs. We demonstrated that the model effectively captures the evolution of energy components over cosmic time, supporting its validity as an alternate explanation for the observed acceleration of the Universe.