Perturbations in Non-Flat Cosmology for $f(T)$ gravity

TL;DR

This paper investigates cosmological perturbations in non-flat FLRW backgrounds within $f(T)$ gravity, analyzing how curvature influences perturbative modes and comparing results to flat cosmology.

Contribution

It extends perturbation analysis in $f(T)$ gravity to non-flat geometries, identifying propagating modes and general behaviors for arbitrary $f(T)$ models.

Findings

Perturbative modes are characterized for positively and negatively curved FLRW backgrounds.

Propagating modes are identified and related to flat cosmology cases.

The behavior of perturbations depends on the spatial curvature in $f(T)$ gravity.

Abstract

The study of cosmological perturbation theory in $f(T)$ gravity is a topic of great interest in teleparallel gravity since this is one of the simplest generalizations of the theory that modifies the teleparallel equivalent of general relativity. In this work, we explore the possibility of a non-flat FLRW background solution and perform perturbations for positively as well as negatively curved spatial geometries, together with a comparison to the flat case. We determine the generalized behaviour of the perturbative modes for this non-flat FLRW setting for arbitrary $f(T)$ models, when the most general homogeneous and isotropic background tetrads are used. We also identify propagating modes in this setup, and relate this with the case of a flat cosmology.