Linear perturbations in vector inflation and stability issues

We continue the analysis of perturbations in vector inflation. The dominant theme of this paper is the long wavelength limit of perturbations in small fields inflation and the controversial issue of its linear stability. We explain the nature of longitudinal modes, describe how they evolve, and show that they are not as harmful as it could seem at the first glance. On the other hand, the gravitational waves' instability in large fields models is shown explicitly. It strongly limits a potential applicability of the recently proposed -type approach to vector inflationary perturbations. Finally, we expose a problem of an extra (gravitational) degree of freedom which appears whenever the vector fields are nonminimally coupled to gravity.