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 ε to the ultraviolet cutoff scale, while tachyons and possibly ghosts do exist for three-dimensional momenta less than ε. 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.
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