Scalar perturbation potentials in a homogeneous and isotropic Weitzenb\"ock geometry

TL;DR

This paper develops gauge-invariant equations for scalar perturbations in teleparallel gravity, using tetrad perturbations and Stewart lemma, to better understand cosmological fluctuations in this alternative gravity theory.

Contribution

It introduces a gauge-invariant formalism for scalar perturbations in teleparallel gravity using tetrad variations and Stewart lemma, advancing cosmological perturbation analysis in this framework.

Findings

Derived gauge-invariant scalar perturbation potentials.

Presented gauge-invariant evolution equations for these potentials.

Clarified the role of tetrad perturbations in cosmological fluctuations.

Abstract

We describe the fully gauge invariant cosmological perturbation equations in teleparallel gravity by using the gauge covariant version of the Stewart lemma for obtaining the variations in tetrad perturbations. In teleparallel theory, perturbations are the result of small fluctuations in the tetrad field. The tetrad transforms as a vector in both its holonomic and anholonomic indices. As a result, in the gauge invariant formalism, physical degrees of freedom are those combinations of perturbation parameters which remain invariant under a diffeomorphism in the coordinate frame, followed by an arbitrary rotation of the local inertial (Lorentz) frame. We derive these gauge invariant perturbation potentials for scalar perturbations and present the gauge invariant field equations governing their evolution.