The dynamical analysis of a parameterized dark energy cosmological model in the f(R,G) gravity

In this paper, we investigate the dynamical behavior of the universe with a flat FLRW model in f(R,G) gravity, where R and G both signify the Ricci scalar and Gauss-Bonnet invariant. Furthermore, in order to determine the model's behavior, it must have the late-time universe's behavior, which involves both an accelerated expansion as well as ending in a big rip. We present a model that begins with a point-type singularity, i.e. a point with zero volume and infinite energy density, by using parametrization of the scale factor a(t). The model's actions are accelerating and expanding at the moment, and ?CDM in late times. Our extensive analysis encompasses the energy conditions, dynamics of certain model solutions and additional cosmological tests through a dominant model. Finally, the proposed framework acts exactly like a quintessence dark energy model in the current time and is reliable with standard cosmology ?CDM in late times.