Spectrum of Perturbations in Anisotropic Inflationary Universe with
  Vector Hair
  We study both the background evolution and cosmological perturbations of
anisotropic inflationary models supported by coupled scalar and vector fields.
The models we study preserve the U(1) gauge symmetry associated with the vector
field, and therefore do not possess instabilities associated with longitudinal
modes (which instead plague some recently proposed models of vector inflation
and curvaton). We first intoduce a model in which the background anisotropy
slowly decreases during inflation; we then confirm the stability of the
background solution by studying the quadratic action for all the perturbations
of the model. We then compute the spectrum of the $h_{\times}$ gravitational
wave polarization. The spectrum we find breaks statistical isotropy at the
largest scales and reduces to the standard nearly scale invariant form at small
scales. We finally discuss the possible relevance of our results to the large
scale CMB anomalies.
