Cosmological solutions of open FLRW metric in f(R,G) gravity: Observational aspects

We investigate the cosmic evolution of the universe in context of Formula: see text gravity with homogeneous and isotropic background, where Formula: see text represents the Ricci scalar, and Formula: see text denotes the Gauss–Bonnet invariant. With the field equations of the Formula: see text gravity in the non-flat spacetime, we examine the characteristics of model with two distinct forms: Formula: see text and Formula: see text, where Formula: see text, Formula: see text, Formula: see text and Formula: see text are the model parameters. The power-law solutions for the field equations are obtained by constraining the model parameters by employing Bayesian analysis tools in conjunction with the Markov Chain Monte Carlo (MCMC) method. We constraint the parameters by utilizing the combined datasets (OHDFormula: see textFormula: see textFormula: see textBAOFormula: see textFormula: see textFormula: see textPantheon) for open Friedmann–Lemaitre–Robertson–Walker (FLRW) model. The parameters of power-law solutions are determined as Formula: see text and Formula: see text. The present dark energy model estimates Formula: see text value higher than the Formula: see textCDM model. This is one of the motivations to consider the Formula: see text gravity to describe dark energy era. The best-fit values of model parameters in an open model yield the power index of power-law solution as Formula: see text. In the present model, the joint analysis by incorporating data from OHD, BAO, and Pantheon datasets favors the open FLRW model with power-law solutions at the late times. The behavior of cosmological parameters has been studied to explore the evolution of dark energy. The equation of state parameter (Formula: see text) supports the accelerated expansion of the Universe at late times. The energy conditions are also studied to test the cosmological viability of the model.