Abstract
Any new gravitational theories can be built with the help of a gauge theory with local Poincare symmetry. This local Poincare symmetry can set up a space-time with torsion. In the present study, the authors working on the parametrization approach towards Hubble’s parameter in the frame of modified teleparallel Gauss-Bonnet gravity which is established on the torsion invariant T and the teleparallel equivalent of the Gauss-Bonnet term TG, say F(T,TG) gravity. In particular, gravity is responsible for an integrated explanation of the cosmological history from early-time inflation to late-time acceleration expansion, by lacking the addition of a cosmological constant. The domino effect acquired is reliable with recent cosmological outcomes. A transition scenario from a decelerating phase to an accelerating phase of cosmic evolution has been detected. Using the combined datasets (SNe-Ia+BAO+CMB+H(z)), we have constrained the transition redshift zt (at which the universe transit from a decelerating phase to an accelerating) and established the best fit value of zt. Next, we paralleled the renovated results of q(z) and ω(z) and found that the outcomes are well-suited with a ΛCDM universe.