Non-Singular Bouncing Model in Energy Momentum Squared Gravity

TL;DR

This paper investigates a non-singular bouncing universe model within a modified gravity framework involving Gauss-Bonnet and energy-momentum squared terms, demonstrating conditions for a viable bounce through analytical and graphical analysis.

Contribution

It introduces a novel $f( ext{G}, ext{T}^2)$ gravity model with specific functional forms and analyzes its capability to produce a non-singular bounce, extending previous bouncing cosmology studies.

Findings

Successful realization of a bouncing universe in the model.

Energy conditions are satisfied during the bounce.

Graphical analysis supports the viability of the proposed model.

Abstract

This work is concerned to study the bouncing nature of the universe for an isotropic configuration of fluid $\mathcal{T}_{\alpha\beta}$ and Friedmann-Lema\^{i}tre-Robertson-Walker metric scheme. This work is carried out under the novel $f(\mathcal{G},\mathcal{T}_{\alpha \beta} \mathcal{T}^{\alpha \beta})$ gravitation by assuming a specific model i.e, $f(\mathcal{G},\mathcal{T}^2)=\mathcal{G}+\alpha \mathcal{G}^2+2\lambda \mathcal{T}^2$ with $\alpha$ and $\lambda$ are constants, serving as free parameters. {The terms $\mathcal{G}$ and $\mathcal{T}^2$ served as an Gauss-Bonnet invariant and square of the energy-momentum trace term as an inclusion in the gravitational action respectively, and is proportional to $\mathcal{T}^2=\mathcal{T}_{\alpha \beta} \mathcal{T}^{\alpha \beta}$.} A specific functional form of the Hubble parameter is taken to provide the evolution of cosmographic parameters. A well known equation of state parameter, $\omega(t)=-\frac{k \log (t+\epsilon )}{t}-1$ is used to represent the dynamical behavior of energy density, matter pressure and energy conditions. A detailed graphical analysis is also provided to review the bounce. Furthermore, all free parameters are set in a way, to make the supposed Hubble parameter act as the bouncing solution and ensure the viability of energy conditions. Conclusively, all necessary conditions for a bouncing model are checked.