Power law cosmology in Gauss-Bonnet gravity with pragmatic analysis

In this study, we present an approach $f(R, G)$ gravity incorporating power law in $G$. To study the cosmic evolution of the universe given by the reconstruction of the Hubble parameter given by $E(z) = \bigg( 1+\frac{z(\alpha+(1+z)^{\beta})}{2 \beta + 1} \bigg)^{\frac{3}{2 \beta}}$. Subsequently, we use various recent observational datasets of OHD, Pantheon, and BAO to estimate the model parameters $H_0,~\alpha$, and $\beta$ applying the Markov Chain Monte Carlo (MCMC) technique in the emcee package to establish the validity of the model. In our findings, we observe that our model shows consistency with standard $\Lambda$CDM, transits from deceleration to acceleration, and enters the quintessence region in late times. The cosmological model satisfies necessary energy constraints, simultaneously violating the strong energy condition (SEC), indicating a repulsive nature and consistent with accelerated expansion. The cosmic evolution of the Hawking temperature and the total entropy for the various observational datasets also show the validity of the model. Thus, our established model demonstrates sufficient potential for explicitly describing cosmological models.