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It is explained that any scalar field in $f(R,T)$ gravity model could presenta new subclass of the k-essence model for inflation. While the case of thequintessence has been studied, there is an empty gap required to be filled byinvestigating more types of field models. Here, we are aiming to partially fillthe gap and concentrate on the tachyon field. In this study, we explore thephenomenon of tachyon inflation in the context of the alternative gravitytheory $f(R,T) = R + \eta T$. By applying slow-roll approximations, we examinethe model in detail for three different potentials: power-law, generalizedT-mode, and inverse hyperbolic cosh. Using observational data and Pythoncoding, we determine a range of values for the model's free parameters thatallow it to fit the data perfectly. In essence, this study provides acomprehensive analysis of tachyon inflation in the $R + \eta T$ gravity theory,offering new insights into this alternative framework and its potential toexplain tachyon inflation.

Exploring new subclass of k-inflation: tachyon inflation in $R+\eta T$ gravity model