Abstract
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 [Formula: see text] where Φ is a density built out of degrees of freedom, the "measure fields" independent of gμν and matter fields appearing in L1, L2. If L1 contains the curvature, scalar potential V(ϕ) and kinetic term for ϕ, L2 another potential for ϕ, U(ϕ), 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(ϕ)=f1eαϕ and U(ϕ)=f2e2αϕ. In the CEF the scalar field potential energy V eff (ϕ) has, in addition to a minimum at zero, a flat region for αϕ→∞, with nonzero vacuum energy, which is suitable for either a new inflationary scenario for the early universe or for a slowly rolling decaying Λ-scenario for the late universe, where the smallness of the vacuum energy can be understood as a kind of seesaw mechanism.
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