\begin{document}$ f (T,\mathcal{T}) $\end{document}theory of gravity, where f is a general function of the torsion scalar T and the trace \begin{document}$ \mathcal{T} $\end{document} of the energy-momentum tensor. It is assumed that the conditions of slow-roll inflation are applicable in \begin{document}$ f (T,\mathcal{T}) $\end{document} gravity. To determine different observables related to inflation, such as the tensor-to-scalar ratio r, scalar spectral index \begin{document}$ n_s $\end{document}, spectral index \begin{document}$ \alpha_s $\end{document}, and tensor spectral index \begin{document}$ n_t $\end{document}, the Hubble slow-roll parameters are utilized for a particular model of \begin{document}$ f (T,\mathcal{T}) $\end{document}. Lastly, an assessment is carried out to determine the feasibility of the models by conducting a numerical analysis of the parameters. The findings indicate that it is feasible to achieve compatibility with the observational measurements of slow-roll parameters by utilizing different values of the free parameters."> Slow-roll inflation in <inline-formula><tex-math id="M1">\begin{document}${\boldsymbol f(T,\mathcal{T})} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/c73b0d9c-1860-4e24-a041-c02710219d39/CPC-2023-0253_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/c73b0d9c-1860-4e24-a041-c02710219d39/CPC-2023-0253_M1.png"/></alternatives></inline-formula> modified gravity -
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