Hubble Tension and Dark Energy in Teleparallel Gauss-Bonnet Gravity: New Constraints from DESI BAO, Pantheon$^+$ and Hubble Data

Abstract: 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 $T_{\mathcal{G}}$, 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 $H(z)$. Bayesian Markov chain Monte Carlo analysis, incorporating late-time observations from Cosmic Chronometers, Pantheon$<sup>+$ with SH0ES, and DESI BAO (Data Release 1 and Data Release 2), constrains the model parameters, revealing that $f(T, T_{\mathcal{G}})$ mimics dark energy in the absence of a cosmological constant, presenting a viable alternative to $Λ$CDM paradigm. Stability is confirmed via scalar perturbation analysis of Hubble and matter density fluctuations, positioning $f(T, T_{\mathcal{G}})$ gravity as a robust framework to address cosmic acceleration challenges. The model yields a present-day effective equation of state $ω<em>{\mathrm{eff}}(z=0) \approx -0.664$ to (-0.693), consistent with observations, and partially alleviates the Hubble tension with $H_0$ estimates of 69 to 71.5\kms. These findings highlight the potential of $f(T, T</em>{\mathcal{G}})$ gravity to resolve fundamental cosmological puzzles while aligning with late-time observational data.