Power-law solutions in $f(T)$ gravity

TL;DR

This paper investigates specific power-law solutions within $f(T)$ gravity, deriving the corresponding Friedmann equations and exploring conditions for phantom phase solutions, thereby expanding understanding of torsion-based cosmological models.

Contribution

It derives explicit $f(T)$ functions for power-law solutions and analyzes their behavior during phantom phases, providing new exact solutions in $f(T)$ gravity.

Findings

Explicit $f(T)$ functions for power-law solutions

Existence of phantom phase solutions in $f(T)$ gravity

Conditions under which power-law solutions occur

Abstract

We have considered an action of the form $T+f(T)+L_m$ describing Einstein's gravity plus a function of the torsion scalar. By considering an exact power-law solution we have obtained the Friedmann equation as a differential equation for the function $f(T)$ in spatially flat universe and obtained the real valued solutions of this equation for some power-law solutions. We have also studied the power-law solutions when the universe enters a Phantom phase and shown that such solutions may exist for some f(T) solutions.