Dynamics of the universe in f(G,τ2) gravity via well-known cosmological bouncing

Abstract

In this manuscript, we consider the newly proposed modified theory in which topological invariant Gauss–Bonnet $G$ is coupled with the energy–momentum squared $({\tau }^2={\tau }_{\mu \nu }{\tau }^{\mu \nu })$. For this matter-geometric coupling, we consider $f(G,{\tau }^2)=f\left(G\right)+g\left({\tau }^2\right)$ model for flat FriedmannRobertsonWalker (FRW) universe. The dynamics of bouncing cosmology are thoroughly examined within the framework of underlying viable model which can overcome the singularity’s challenge in standard Big-Bang cosmology. We study a power law scale factor and some cosmological bouncing scale factors such as symmetric, super, oscillatory and matter. These cosmological bouncing scale factors are essential for exploring the universe’s origins while bypassing the concept of an initial singularity, thus presenting alternative approaches that address the limitations of the Big Bang model. In this scenario, we determine the equation of state parameter, $\omega$, along with the squared sound speed parameter. Additionally, we investigate the behavior of the $\omega -{\omega }^{\prime }$ plane for underlying framework. Interestingly, it should be noted that every outcome favors recent observational data.