Constant-roll Inflation in $f(T)$ Teleparallel Gravity

TL;DR

This paper explores how the constant-roll condition affects inflation in $f(T)$ teleparallel gravity, providing a reconstruction method, phase space analysis, and compatibility with observational data.

Contribution

It introduces a reconstruction technique for $f(T)$ gravity under constant-roll conditions and analyzes the phase space and observational implications of such models.

Findings

The theory can be compatible with current observational data.

The phase space analysis reveals fixed points and trajectories relevant to inflation.

The reconstruction method links cosmological evolution to specific $f(T)$ functions.

Abstract

We investigate in detail the implications of the constant-roll condition on the inflationary era of a scalar field coupled to a teleparallel $f(T)$ gravity. The resulting cosmological equations constitute a reconstruction technique which enables us to find either the $f(T)$ gravity which corresponds to a given cosmological evolution, or the Hubble rate of the cosmological evolution generated by a fixed $f(T)$ gravity. We also analyze in some detail the phase space of the constant-roll teleparallel gravity and we discuss the physical significance of the resulting fixed points and trajectories. Also we calculate the observational indices of a theory with given $f(T)$ gravity, and we discuss all the implications of the constant-roll condition on these. As we demonstrate, the resulting theory can be compatible with the current observational data, for a wide range of values of the free parameters of the theory.