Abstract:
We present a simple model in which the weak energy condition is violated for
spatially homogeneous, slowly evolving fields. The excitations in Minkowski
space in an external field with violation of the Lorentz invariance do not
contain ghosts, tachyons, or superluminal modes at spatial momenta ranging
from some low scale $\epsilon$ to the ultraviolet cutoff scale, while
tachyons and possibly ghosts do exist for three-dimensional momenta less than
$\epsilon$. We show that in the absence of other matter, a slow-roll
cosmological regime is possible. In this regime, the weak energy condition is
violated, and yet homogeneity and isotropy are not completely spoiled
(at the cost of fine tuning), because for a given conformal
momentum, the tachyon mode increases during a sufficiently short time.
Keywords:Lorentz invariance, vector field, cosmological expansion, weak energy condition.