Cosmological perturbations in f(T) gravity

TL;DR

This paper analyzes cosmological perturbations in f(T) gravity, deriving conditions for stability, studying matter growth, and comparing with General Relativity, revealing differences on large scales and confirming the absence of massive gravitons.

Contribution

It provides a detailed formalism for perturbations in f(T) gravity, including stability constraints and matter growth analysis, extending previous work to include vector and tensor sectors.

Findings

f(T) constant reproduces GR at all perturbation levels

On large scales, matter overdensity evolution differs from LCDM

f(T) gravity is free of massive gravitons with standard vierbein

Abstract

We investigate the cosmological perturbations in f(T) gravity. Examining the pure gravitational perturbations in the scalar sector using a diagonal vierbien, we extract the corresponding dispersion relation, which provides a constraint on the f(T) ansatzes that lead to a theory free of instabilities. Additionally, upon inclusion of the matter perturbations, we derive the fully perturbed equations of motion, and we study the growth of matter overdensities. We show that f(T) gravity with f(T) constant coincides with General Relativity, both at the background as well as at the first-order perturbation level. Applying our formalism to the power-law model we find that on large subhorizon scales (O(100 Mpc) or larger), the evolution of matter overdensity will differ from LCDM cosmology. Finally, examining the linear perturbations of the vector and tensor sectors, we find that (for the standard choice of vierbein) f(T) gravity is free of massive gravitons.