Nonminimal coupling in anisotropic teleparallel inflation

We study an anisotropic inflationary scenario in teleparallel gravity. We consider a model where the inflaton is nonminimally coupled both to torsion and a vector field, which can lead to anisotropic inflation. In the weak-coupling limit, our results coincide with the results obtained in the general relativistic framework. However, in the strong-coupling regime of the Jordan frame, we show that the anisotropy shear to expansion ratio is a constant, and can be much larger than the slow-roll parameter. Applying a conformal transformation we then work in the Einstein frame, which in teleparallel gravity introduces a different form of coupling between the inflaton and torsion. In this frame we show that in the strong coupling regime the anisotropy shear to expansion ratio is a different constant, that can be made suitably small.