- 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 = ∫ L1 Φ d4cursive Greek chi + ∫ L2√-g d4cursive Greek chi where Φ is a density built out of degrees of freedom independent of the metric. For global scale invariance, a "dilaton" φ has to be introduced, with nontrivial potentials V(φ) = f1eαφ in L1 and U(φ) = f2e2αφ in L2. This leads to nontrivial mass generation and a potential for φ 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.