Small dark energy and stable vacuum from Dilaton–Gauss–Bonnet coupling in TMT

• Main Authors: Eduardo I. Guendelman, Hitoshi Nishino, Subhash Rajpoot
• Format: Article
• Language: English
• Published: SpringerOpen 2017-04-01
• Series: European Physical Journal C: Particles and Fields
• Subjects: Cosmological Constant; Vacuum Energy Density; Dilaton Field; Scale Symmetry Breaking; Topological Density
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-017-4808-7

Abstract In two measures theories (TMT), in addition to the Riemannian measure of integration, being the square root of the determinant of the metric, we introduce a metric-independent density $$\Phi $$ Φ in four dimensions defined in terms of scalars $$\varphi _a$$ φ a by $$\Phi =\varepsilon ^{\mu \nu \rho \sigma } \varepsilon _{abcd} (\partial _{\mu }\varphi _a)(\partial _{\nu }\varphi _b) (\partial _{\rho }\varphi _c) (\partial _{\sigma }\varphi _d)$$ Φ = ε μ ν ρ σ ε a b c d ( ∂ μ φ a ) ( ∂ ν φ b ) ( ∂ ρ φ c ) ( ∂ σ φ d ) . With the help of a dilaton field $$\phi $$ ϕ we construct theories that are globally scale invariant. In particular, by introducing couplings of the dilaton $$\phi $$ ϕ to the Gauss–Bonnet (GB) topological density $$\, {\sqrt{-g}} \, \phi \left( R_{\mu \nu \rho \sigma }^2 - 4 R_{\mu \nu }^2 + R^2 \right) \,$$ - g ϕ R μ ν ρ σ 2 - 4 R μ ν 2 + R 2 we obtain a theory that is scale invariant up to a total divergence. Integration of the $$\varphi _a$$ φ a field equation leads to an integration constant that breaks the global scale symmetry. We discuss the stabilizing effects of the coupling of the dilaton to the GB-topological density on the vacua with a very small cosmological constant and the resolution of the ‘TMT Vacuum-Manifold Problem’ which exists in the zero cosmological-constant vacuum limit. This problem generically arises from an effective potential that is a perfect square, and it gives rise to a vacuum manifold instead of a unique vacuum solution in the presence of many different scalars, like the dilaton, the Higgs, etc. In the non-zero cosmological-constant case this problem disappears. Furthermore, the GB coupling to the dilaton eliminates flat directions in the effective potential, and it totally lifts the vacuum-manifold degeneracy.