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

TL;DR

The paper investigates a teleparallel gravity model with action $S=\frac{1}{2\kappa^2}\int e\,f(T, T_{\mathcal{G}})\,d^4x$, deriving modified Friedmann and perturbation equations for a flat FLRW universe. Adopting the minimal nontrivial form $f(T, T_{\mathcal{G}})= -T + \alpha\sqrt{T^2 + \beta T_{\mathcal{G}}}$, the authors solve for $H(z)$ numerically and constrain the parameters via MCMC using CC, Pantheon$^+$, and DESI BAO data, finding $\omega_{\mathrm{eff}}(z=0)\approx -0.66$ to $-0.69$ and $H_0$ in the 69--71.5 km s$^{-1}$ Mpc$^{-1}$ range. The model partially alleviates the Hubble tension while remaining consistent with late-time observations, and linear perturbation analysis demonstrates stability with decaying Hubble and matter perturbations. These results position $f(T, T_{\mathcal{G}})$ gravity as a robust alternative to $\Lambda$CDM for explaining cosmic acceleration, with growth history and future surveys offering avenues for further discrimination.

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$^+$ 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 $ω_{\mathrm{eff}}(z=0) \approx -0.664$ 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 $f(T, T_{\mathcal{G}})$ gravity to resolve fundamental cosmological puzzles while aligning with late-time observational data.

Figures (5)

• Figure 1: The contour plots display the $1\sigma$ and $2\sigma$ uncertainty regions for the model parameters $H_0$, $\Omega_{\mathrm{m}0}$, $\alpha$, $\beta$, $\gamma$ and $M$. These contours are based on the combined CC+PPS, CC+PPS+BAO$_1$, CC+PPS+DESI DR1 and CC+PPS+DESI DR2 datasets.
• Figure 2: Behavior of the deceleration parameter using the combined datasets.
• Figure 3: Behavior of the dark energy EoS parameter using the combined datasets.
• Figure 4: A whisker plot illustrating the Hubble constant ($H_0$) parameter, highlighting discrepancies between early-time and late-time measurements, $\Lambda$CDM and $f(T, T_{\mathcal{G}})$ models.
• Figure 5: Evolution of the Hubble perturbation parameter $\delta(t)$ (left panel) and the matter perturbation parameter $\delta_{\mathrm{m}}(t)$ (right panel) as a function of cosmic time in the $f(T, T_\mathcal{G})$ gravity model.