General cosmological perturbations in teleparallel gravity

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.

18 pages, no figures; invited contribution to the Eur. Phys. J. Plus focus point "Modified Gravity Theories and Cosmology"; updated references to accepted version

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• Teleparallel Gravity: From Theory to Cosmology
• Revisiting Cosmologies in Teleparallelism
• Perturbations in Non-Flat Cosmology for $f(T)$ gravity
• The effective field theory approach to the strong coupling issue in $f(T)$ gravity
• Teleparallel axions and cosmology
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• Spherically symmetric teleparallel geometries
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• Ghost and Laplacian Instabilities in the Teleparallel Horndeski Gravity
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