Scale invariance, new inflation and decaying Λ-terms

Realizations of scale invariance are studied 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, the "measure fields" independent of g(mu nu), and matter fields appearing in L-1, L-2. If L-1 contains the curvature, scalar potential V(phi) and kinetic term for phi, L-2 another potential for phi, U(phi), then the true vacuum state has zero energy density, when theory is analyzed in the conformal Einstein frame (CEF), where the equations assume the Einstein form. Global scale invariance is realized when V(phi) = f1e(alpha phi) and U(phi) = f2e(2 alpha phi). In the CEF the scalar field potential energy V-eff(phi) has, in addition to a minimum at zero, a flat region for alpha phi --> infinity, with nonzero vacuum energy, which is suitable for either a new inflationary scenario for the early universe or for a slowly rolling decaying Lambda-scenario for the late universe, where the smallness of the vacuum energy can be understood as a kind of seesaw mechanism.