Scale invariance and vacuum energy

The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. Scale invariance is considered in the context of a gravitational theory where the action, in the first-order formalism, is of the form S = integral L-1 Phi d(4)x + integral L(2)root - gd(4)x where Phi is a density built out of degrees of freedom independent of the metric. For global scale invariance, a "dilaton" phi has to be introduced, with nontrivial potentials V(phi) = f(1)e(alpha phi) in L-1 and U(phi) = f(2)e(2 alpha phi) in L-2. This leads to nontrivial mass generation and a potential for phi which is interesting for new inflation. Scale invariant mass terms for fermions lead to a possible explanation of the present day accelerated universe and of cosmic coincidences.