Inflation with stable anisotropic hair: is it cosmologically viable?
  Recently an inflationary model with a vector field coupled to the inflaton
was proposed and the phenomenology studied for the Bianchi type I spacetime. It
was found that the model demonstrates a counter-example to the cosmic no-hair
theorem since there exists a stable anisotropically inflationary fix-point. One
of the great triumphs of inflation, however, is that it explains the observed
flatness and isotropy of the universe today without requiring special initial
conditions. Any acceptable model for inflation should thus explain these
observations in a satisfactory way. To check whether the model meets this
requirement, we introduce curvature to the background geometry and consider
axisymmetric spacetimes of Bianchi type II,III and the Kantowski-Sachs metric.
We show that the anisotropic Bianchi type I fix-point is an attractor for the
entire family of such spacetimes. The model is predictive in the sense that the
universe gets close to this fix-point after a few e-folds for a wide range of
initial conditions. If inflation lasts for N e-folds, the curvature at the end
of inflation is typically of order exp(-2N). The anisotropy in the expansion
rate at the end of inflation, on the other hand, while being small on the
one-percent level, is highly significant. We show that after the end of
inflation there will be a period of isotropization lasting for about 2N/3
e-folds. After that the shear scales as the curvature and becomes dominant
around N e-folds after the end of inflation. For plausible bounds on the reheat
temperature the minimum number of e-folds during inflation, required for
consistency with the isotropy of the supernova Ia data, lays in the interval
(21,48). Thus the results obtained for our restricted class of spacetimes
indicates that inflation with anisotropic hair is cosmologically viable.
