Testing Unimodular Gravity
  We consider models of gravitation that are based on unimodular general
coordinate transformations (GCT). These transformations include only those
which do not change the determinant of the metric. We treat the determinant as
a separate field which transforms as a scalar under unimodular GCT. We consider
a class of such theories. In general, these theories do not transform
covariantly under the full GCT. We characterize the violation of general
coordinate invariance by introducing a new parameter. We show that the theory
is consistent with observations for a wide range of this parameter. This
parameter may serve as a test for possible violations of general coordinate
invariance. We also consider the cosmic evolution within the framework of these
models. We show that in general we do not obtain consistent cosmological
solutions if we assume the standard cosmological constant or the standard form
of non-relativistic matter. We propose a suitable generalization which is
consistent with cosmology. We fit the resulting model to the high redshift
supernova data. We find that we can obtain a good fit to this data even if
include only a single component, either cosmological constant or
non-relativistic matter.
