An anisotropic cosmological model with Bianchi type III universe in f(G) gravity

The paper is devoted to exploring the exact solution of the modified Einstein's field in the setting of spatially homogeneous and anisotropic Bianchi type III spacetime in modified f(G) gravity, where G is Gauss-Bonnet invariant. Here, by employing the hyperbolic hybrid scale factor a = emt (sinh(t))n in which m,n are positive constants, with the power-law f (G)=βGm+1 model where β,m are arbitrary constants, we computed the physical and geometrical properties of the cosmological parameters of the model. The results of the model parameters are well satisfied with recent cosmological observational data. To get the exact solution of the field equation of the Bianchi type III model in the presence of an anisotropic dark fluid, we consider the relation in which the shear scalar (σ) is proportional to the expansion scalar (θ), resulting in C = An. Furthermore, the energy conditions for the power-law f(G) model are graphically examined, and it turns out that the null energy condition (NEC), weak energy condition (WEC), and dominant energy condition (DEC) are well satisfied except for the strong energy condition (SEC). The violation of the strong energy conditions (SEC) indicates the f(G) model supports the universe's current expansion with negative pressure, having a quintessence model in the present and Λ cold dark matter (CDM) model in the future.