Cosmological implications of unimodular gravity

We consider a model of gravity and matter fields which is invariant only under unimodular general coordinate transformations (GCT). The determinant of the metric is treated as a separate field which transforms as a scalar under unimodular GCT. Furthermore we also demand that the theory is invariant under a new global symmetry which we call generalized conformal invariance. We study the cosmological implications of the resulting theory. We show that this theory gives a fit to the high-z supernova data which is identical to the standard Big Bang model. Hence we require some other cosmological observations to test the validity of this model. We also consider some models which do not obey the generalized conformal invariance. In these models we can fit the supernova data without introducing the standard cosmological constant term. Furthermore these models introduce only one dark component and hence solve the coincidence problem of dark matter and dark energy.