Late time phenomena in $$f(T,{\mathcal {T}})$$ gravity framework: role of $$H_0$$ priors

Abstract This study explored the behavior of the $$f(T, {\mathcal {T}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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+ &amp;SH0ES (with SH0ES) data sets. Additionally, we incorporated data from BAO along with $$H_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> priors. We observed that integrating SH0ES data points leads to a higher estimation of $$H_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> 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 $$\chi ^2_{min}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>χ</mml:mi> <mml:mrow> <mml:mi>min</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> value for each combination of data sets to evaluate the chosen model against the standard $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model. Our primary finding is that the various dataset combinations in the $$f(T, {\mathcal {T}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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 $$f\sigma _8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:mrow> </mml:math> using these findings. We plotted the cosmological background parameters to check the behavior of the $$f(T, {\mathcal {T}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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.