FRW in quadratic form of $f(T)$ gravitational theories

TL;DR

This paper derives an asymptotic solution for a homogeneous, isotropic universe in quadratic $f(T)$ gravity, showing how higher torsion order can explain late-time cosmic acceleration and affect cosmological evolution.

Contribution

It introduces an asymptotic solution for quadratic $f(T)$ gravity and explores its implications for late universe acceleration.

Findings

Higher torsion order can drive late accelerated expansion.

The scalar torsion $T$ varies with cosmic time in the solution.

Quadratic $f(T)$ influences cosmological behavior for different equations of state.

Abstract

We derive asymptote solution of a homogeneous and isotropic universe governed by the quadratic form of the field equation of $f(T)$ gravity. We explain how the higher order of the torsion can provide an origin for late accelerated phase of the universe in the FRW. The solution makes the scalar torsion $T$ to be a function of the cosmic time $t$. We show that for the equation of state $p=\omega \rho$ with $\omega\neq -1$ the scale factor represent late phase of universe. We perform the cosmological studies and show how the quadratic form of $f(T)$ effect on the behavior of these studies.