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

TL;DR

This paper investigates tachyon inflation within the $f(R,T) = R +  T$ gravity model, analyzing its compatibility with observational data for various potentials and highlighting its potential as an alternative inflationary framework.

Contribution

It introduces a new subclass of k-inflation via tachyon fields in the $f(R,T)$ gravity model, filling a gap in the study of scalar field inflation models.

Findings

Model fits observational data with specific parameter ranges.

Analyzes three potentials: power-law, generalized T-mode, inverse hyperbolic cosh.

Provides a comprehensive framework for tachyon inflation in $f(R,T)$ gravity.

Abstract

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