Vector field instability and the primordial tensor spectrum

It has recently been shown that the presence of a spectator pseudoscalar field, coupled to photons through a Chern-Simons term, can amplify the primordial tensor spectrum without observationally disrupting the primordial scalar spectrum. The amplification occurs due to an instability that develops for the vector fields. We consider the extension of previous studies to account for the contribution arising from an inhomogeneous vector background which is generated prior to the onset of inflation. We find that there may be contributions in which net momentum is transferred between the inhomogeneous vector background and the gravitons, which would give rise to a signature different than in the absence of the semiclassical corrections. We discuss the properties the classical vector field form must have in order for these signatures to leave observable imprints, though we were unable to construct a model for generating such a vector field.