  Short distance structure of spacetime may show up in the form of high
freqency dispersion. Although such dispersion is not locally Lorentz invariant,
we show in a scalar field model how it can nevertheless be incorporated into a
generally covariant metric theory of gravity provided the locally preferred
frame is dynamical. We evaluate the resulting energy-momentum tensor and
compute its expectation value for a quantum field in a thermal state. The
equation of state differs at high temperatures from the usual one, but not by
enough to impact the problems of a hot big bang cosmology. We show that a
superluminal dispersion relation can solve the horizon problem via superluminal
equilibration, however it cannot do so while remaining outside the Planck
regime unless the dispersion relation is artificially chosen to have a rather
steep dependence on wavevector.
