f(T, T_G) gravity theory: observational constraints for Barrow holographic dark energy with Hubble and Granda-Oliveros cutoff

Abstract The reconstruction technique and stability of various well-known cosmological parameters of f ( T , T G ) gravity are investigated in this paper, where T and T G denote the torsion scalar and Gauss-Bonnet invariant torsion component. In this model, we consider Barrow holographic dark energy (BHDE) as candidates of IR cut-offs and develop the corresponding field equations. In our analysis, we have examined two well-known IR cutoffs Hubble and GrandaOliveros (GO) cutoffs. Our findings indicate a transition from a deceleration phase to an accelerated phase in the Universe for both cutoff scenarios, aligning with recent observational data. A reconstruction method is introduced to analyze the parameters linked to BHDE within the framework of viscous cosmology. Our investigation revealed that the power-law cosmology effectively aligns with the observational datasets. By combining the Markov Chain Monte Carlo (MCMC) technique with Bayesian analysis and likelihood function, we were able to determine the model parameters H 0 = 69.6 ± 1.8 km/s/Mpc; q = − 0.281 ± 0.034 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic">M</mml:mi> </mml:math> = 23.846 ± 0.010. We have solved the modified Einstein’s field equations by taking the bulk-viscosity component ξ = ξ 0 + ξ 1 H . Additionally, we have examined the energy conditions to assess the consistency of our model.