Hubble tension and dark energy in teleparallel Gauss-Bonnet gravity: new constraints from DESI BAO, Pantheon+ and Hubble data

We explore the cosmological dynamics of a teleparallel Gauss-Bonnet gravity model defined by the torsion scalar T and the torsion-based Gauss-Bonnet invariant T𝒢, deriving modified Friedmann equations for a flat FLRW Universe and corresponding linear scalar perturbation equations. Using a numerical approach, we solve these equations for pressureless matter, predicting the redshift evolution of the Hubble parameter H(z). Using a Bayesian Markov chain Monte Carlo analysis based on late-time observations from Cosmic Chronometers, Pantheon+ without SH0ES, and DESI BAO Data Release 1 and Data Release 2, we constrain the model parameters and show that this class of f(T,T𝒢) cosmologies can mimic an effective dark-energy component without introducing an explicit cosmological constant. We further examine the scalar perturbation sector of the posterior-supported cosmological branch and find that the solutions considered in this work remain well-behaved within the adopted perturbative treatment. The model yields a present-day effective equation-of-state parameter in the range ωeff(z = 0) ≈ -0.664 to -0.693, consistent with late-time observations, and shifts the inferred value of H0 toward 69–71.5 km s-1 Mpc-1, suggesting a partial alleviation, though not a complete resolution, of the Hubble tension.