Late Time Phenomena in $f(T,\mathcal{T})$ Gravity Framework: Role of $H_0$ Priors

Abstract: This study explored the behavior of the $f(T, \mathcal{T})$ cosmological model with the use of various data set combinations. We also compared the results for this model between the Pantheon+ (without SH0ES) and the Pantheon+&SH0ES (with SH0ES) data sets. Additionally, we incorporated data from BAO along with $H_0$ priors. We observed that integrating SH0ES data points leads to a higher estimation of $H_0$ than Pantheon+ (without SH0ES). We perform an extensive MCMC analysis for each combination of data sets, providing constraints on the model parameters. We also computed the $\chi<sup>2_{min}$ value for each combination of data sets to evaluate the chosen model against the standard $\Lambda$CDM model. Our primary finding is that the various dataset combinations in the $f(T, \mathcal{T})$ model we examined relate to a range of Hubble constants, which could contribute to reducing the cosmic tension associated with this parameter. Additionally, we investigate the evolution of matter fluctuations by solving the density contrast evolution equation numerically. We calculate numerical solutions for the weighted growth rate $f\sigma_8$ using these findings. We plotted the cosmological background parameters to check the behavior of the $f(T, \mathcal{T})$ model in late-time. Based on the behavior of these background cosmological parameters, we conclude that our selected models reflect the late-time cosmic dynamics of the Universe.