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 = ∫L₁Φd⁴cursive Greek chi + ∫L₂√-gd⁴cursive Greek chi where Φ is a density built out of degrees of freedom, the "measure fields" independent of g_μν 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) = f₁e^αφ and U(φ) = f₂e^2αφ. 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.