Spin connection and cosmological perturbations in $f(T)$ gravity

Understand

In this paper we study cosmological perturbations in teleparallel gravity.

• We discuss problems which appear in standard approach to $f(T)$ gravity, and find that these problems may be solved within covariant formulation of teleparallel gravity, which take into account spin connection.
• We calculate spin connection which symmetrize equation for perturbation and split diagonal and non-diagonal part of equation of motion.
• We demonstrate that there is minimal solution for spin connection, which lead to zero slip, however, in this case one additional equation appears, so the system may become over-determined.