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Inspired by high-energy physics and by considering standard gravity theory as the low-energy limit of quantum theory, the modification of general relativity as R + f (G) has been proposed. This paper is dedicated to investigating the cosmological model of modified Gauss–Bonnet gravity in four dimensions. General field equations for the four-dimensional Friedmann– Robertson–Walker metric are given in detail. Also, it is well known that Hubble parameter H (z) measurements are helpful for the inference of cosmological model parameters. We try to explain the MCMC statistical approach used to calculate Hubble's parameter. The resulting form of H (z) was limited using Cosmic Chronometric data, Standard Candles SN Ia from Pantheon, and Baryon Acoustic Oscillations to obtain the best match values by using the regression equation. Finally, to examine the late-time dynamics of our Universe, the behavior of physical and kinematic variables like the deceleration parameter (q) , State-finder parameters { r , s } , diagnostic parameter ( O m (z)), equation of state parameter as well as the behavior of energy conditions versus redshift with the parameter values are presented. [ABSTRACT FROM AUTHOR]

In the present study, we have obtained cosmological models with variable deceleration parameter q = r(t) and polytropic equation of state p = ωρ2 - ρ in the framework of Kantowski-Sachs universe. A new class of exact solutions has been obtained by assuming deceleration parameter as a variable. Here we discussed models for two cases polynomial and exponential. The physical aspects of these models have also been investigated. [ABSTRACT FROM AUTHOR]