A cosmological probe in a theory of higher-order gravity

In this work, we study a cosmological model in a modified gravity containing the Ricci scalar $R$ and the Gauss–Bonnet invariant $G$ in a linear combination. We establish the model by using a model’s unconventional technique by parameterizing the scale factor, in which the model begins with a finite spatial volume at the time of the early evolution of the Universe and exhibits an accelerating expansion at later times. The expansion of the Universe transitions from an early decelerating state to a late-time accelerating state. We use the various diagnostic techniques to examine the stability of the model. The prime goal of studying the model is to obtain precise cosmological constraints for $H_0$, $\alpha$, and $t_0$, and discuss the various physical features of the model according to constrained model parameters. Finally, we find that our model is a stable expanding and accelerating quintessence dark energy model in late times.