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

We investigate the cosmic evolution of the universe in context of f(R, G) gravity with homogeneous and isotropic background, where R represents the Ricci scalar, and G denotes the Gauss-Bonnet invariant. With the field equations of the f(R, G) gravity in the non-flat spacetime, we examine the characteristics of model with two distinct forms: f(1)(R, G) = mu R(n)G(m) and f(2)(R, G) = beta R-1+beta(2)mu R(n)G(m), where n, m, beta(1) and beta(2) 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 (MC) method. We constraint the parameters by utilizing the combined datasets (OHD+BAO+Pantheon) for open Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The parameters of power-law solutions are determined as H-0 = 70.76732(-0.00088)(+0.00010) km/(s & sdot; Mpc) and q = -0.6478(-0.000075)(+0.000091). The present dark energy model estimates H-0 value higher than the Lambda CDM model. This is one of the motivations to consider the f(R, G) 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 alpha = 2.394949(-0.00060)(+.000089). 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 (omega similar or equal to-1) supports the accelerated expansion of the Universe at late times. The energy conditions are also studied to test the cosmological viability of the model.