Dominance of a Dynamical Measure and Disappearance of the Cosmological Constant

Abstract

We consider an action which consists of two terms: the first S_{1}=\int L_{1}Φd^{4}x and the second S_{2}=\int L_{2}\sqrt{-g}d^{4}x where Φis a measure which has to be determined dynamically. S_{1} satisfies the requirement that the transformation L_{1}\to L_{1}+const does not effect equations of motion. In the first order formalism, a constraint appears which allows to solve χ=Φ/\sqrt{-g}. Then, in a true vacuum state (TVS), χ\to\infty and in the conformal Einstein frame no singularities are present, the energy density of TVS is zero without fine tuning of any scalar potential in S_{1} or S_{2}. When considering only a linear potential for a scalar field ϕin S_{1}, the continuous symmetry ϕ\toϕ+const is respected. Surprisingly, in this case SSB takes place while no massless ("Goldstone") boson appears.