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.