General cosmological perturbations in teleparallel gravity

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