Classical stability of a homogeneous, anisotropic inflating space-time

Abstract

We study the classical stability of an anisotropic space-time seeded by a spacelike, fixed-norm, dynamical vector field in a vacuum-energy-dominated inflationary era. It serves as a model for breaking isotropy during the inflationary era. We find that, for a range of parameters, the linear differential equations for small perturbations about the background do not have a growing mode. We also examine the energy of fluctuations about this background in flat space. If the kinetic terms for the vector field do not take the form of a field strength tensor squared, then there is a negative energy mode and the background is unstable. For the case where the kinetic term is of the form of a field strength tensor squared, we show that classical solutions to the equations of motion that are close to the background solution have energy greater than or equal to zero. This suggests that the background is metastable.