Matter Density Perturbations in Modified Teleparallel Theories

TL;DR

This paper investigates how matter density perturbations behave in modified teleparallel gravity theories, highlighting the effects of extra degrees of freedom on cosmological scales and their deviation from general relativity.

Contribution

It formulates a comprehensive vierbein perturbation approach and analyzes the impact of new degrees of freedom in $f(T)$ gravity on cosmological perturbations.

Findings

No significant effect of new modes on small-scale perturbations.

Deviations from general relativity appear on super-horizon scales.

Extra degrees of freedom influence large-scale cosmological behavior.

Abstract

We study the matter density perturbations in modified teleparallel gravity theories, where extra degrees of freedom arise from the local Lorentz violation in the tangent space. We formulate a vierbein perturbation with variables addressing all the 16 components of the vierbein field. By assuming the perfect fluid matter source, we examine the cosmological implication of the 6 unfamiliar new degrees of freedom in modified $f(T)$ gravity theories. We find that despite the new modes in the vierbein scenario provide no explicit significant effect in the small-scale regime, they exhibit some deviation from the standard general relativity results in super-horizon scales.