General cosmological perturbations in teleparallel gravity

TL;DR

This paper develops a comprehensive framework for analyzing linear cosmological perturbations in teleparallel gravity, including gauge-invariant variables and the effects of tetrad choices, with applications to various teleparallel theories.

Contribution

It introduces a gauge-invariant perturbation formalism for general teleparallel cosmologies, highlighting the impact of tetrad choices on perturbation behavior.

Findings

Derived gauge-invariant perturbation variables.

Identified new terms depending on tetrad choice.

Applied formalism to teleparallel gravity theories.

Abstract

We discuss linear perturbations of the most general class of teleparallel spacetimes with cosmological symmetry, and perform a decomposition of these perturbations into irreducible components. We then study their behavior under gauge transformations, i.e., infinitesimal diffeomorphisms of the background spacetime, and derive a full set of gauge-invariant perturbation variables. Comparing our results with perturbations around the diagonal tetrad corresponding to a spatially flat teleparallel background cosmology, we see the appearance of new terms which depend on the particular choice of a cosmologically symmetric background tetrad. Finally, we demonstrate the application of our findings to teleparallel gravity theories. For convenience, results are displayed both in general and conformal coordinates.