Cosmological insights from an exponential Om(z) function in f(T,TG) gravity framework

Abstract

We examine a modified teleparallel gravity model defined by $f(T,T_G)=T+\gamma \sqrt{T_G}+\delta \sqrt{T}$ by introducing an exponential $Om\left(z\right)$ diagnostic of the form $Om\left(z\right)=\alpha e^{\frac{z}{1+z}}+\beta$. This novel form captures smooth redshift evolution and allows for a flexible, model-independent probe of dark energy dynamics. We derive a Hubble function from this expression and use MCMC analysis with 31 CC, 26 BAO and 1701 Pantheon+ data points to constrain the model parameters. The best-fit results yield $H_0\in [68.46,77.38]$ km/s/Mpc, $\alpha \in [-0.232,-0.068]$ and $\beta \in [0.218,0.560]$ which is consistent with local $H_0$ values. Statistical model selection using AIC and BIC shows that while our model fits the data comparably to ΛCDM, AIC indicates only moderate disfavor, whereas BIC—due to its stronger penalty for additional parameters—provides strong to very strong evidence in favor of the simpler ΛCDM model. Our model predicts a transition redshift $z_{tr}\approx (0.48-0.54)$, present $q_0\approx -0.34$, and ${\omega }_0\approx -0.33$. It satisfies NEC and DEC, closely tracks ΛCDM in the statefinder plane and estimates a cosmic age of $(13.28-13.87)$ Gyr which confirms its strength in explaining late-time acceleration. Our findings demonstrate that the exponential $Om\left(z\right)$ parameterization provides a robust and insightful approach to trace dark energy evolution within modified gravity frameworks.