Exploring Observational Constraints on F(T , T\(_G\)) Gravity with Hubble’s Parametrization

Abstract

New gravitational theories can be formulated using gauge theory with local Poincar´e symmetry, which naturally leads to a spacetime with torsion. In this study, we explore a parametrization approach to the Hubble parameter within the framework of modified teleparallel Gauss-Bonnet gravity. This theory is based on the torsion invariant T and the teleparallel equivalent of the Gauss-Bonnet term T\(_G\), forming the F(T , T\(_G\)) gravity model. Notably, this modified gravity framework provides a unified explanation of cosmic evolution, encompassing early-time inflation and latetime accelerated expansion, without requiring a cosmological constant. The results obtained from our analysis are consistent with recent cosmological observations, demonstrating a transition from a decelerating phase to an accelerating phase of cosmic expansion. By utilizing a combination of observational datasets, including Type Ia Supernovae (SNe Ia), Baryon Acoustic Oscillations (BAO), Cosmic Microwave Background (CMB), and Hubble parameter H(z) measurements, we have constrained the transition redshift z_t, which marks the epoch when the universe shifts from deceleration to acceleration. Furthermore, we have determined the best-fit value of z_t and compared the reconstructed evolution of the deceleration parameter q(z) and the equation of state parameter \(\omega\)(z). The findings are in strong agreement with the standard \(\Lambda\)CDM model, reinforcing the validity of our approach.