Growth factor in f(T) gravity

TL;DR

This paper derives the growth factor evolution in $f(T)$ gravity, compares it with $ ext{Lambda}$CDM and dark energy models, and finds that perturbations grow slower in $f(T)$ gravity due to weakened gravity effects.

Contribution

It provides the first derivation of the growth factor evolution equation in $f(T)$ gravity and compares its predictions with standard cosmological models.

Findings

Perturbations grow slower in $f(T)$ gravity when $rac{ ext{d}f}{ ext{d}T}>0$.

In the power law model, growth behavior differs from $ ext{Lambda}$CDM at small redshift.

Weakened gravity in $f(T)$ models affects structure formation.

Abstract

We derive the evolution equation of growth factor for the matter over-dense perturbation in $f(T)$ gravity. For instance, we investigate its behavior in power law model at small redshift and compare it to the prediction of $\Lambda$CDM and dark energy with the same equation of state in the framework of Einstein general relativity. We find that the perturbation in $f(T)$ gravity grows slower than that in Einstein general relativity if $\p f/\p T>0$ due to the effectively weakened gravity.