General cosmological perturbations in teleparallel gravity

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.

Automated summary

This paper discusses linear perturbations of teleparallel spacetimes with cosmological symmetry and decomposes them into irreducible components. The behavior of these perturbations under gauge transformations is studied, leading to the derivation of a complete set of gauge-invariant perturbation variables. Comparing the results with perturbations around a diagonal tetrad corresponding to a spatially flat teleparallel background cosmology reveals the appearance of new terms dependent on the specific choice of a cosmologically symmetric background tetrad.