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

Eduardo I. Guendelman; Hitoshi Nishino; Subhash Rajpoot

doi:10.1140/epjc/s10052-017-4808-7

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2017) 77: 240
https://doi.org/10.1140/epjc/s10052-017-4808-7

Regular Article - Theoretical Physics

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

Eduardo I. Guendelman¹^*, Hitoshi Nishino² and Subhash Rajpoot²

¹ Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel
² California State University at Long Beach, Long Beach, CA, USA

^* e-mail: guendel@bgu.ac.il

Received: 2 January 2017
Accepted: 27 March 2017
Published online: 13 April 2017

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 $\Phi$ in four dimensions defined in terms of scalars $\varphi _a$ by $\Phi =\varepsilon ^{\mu \nu \rho \sigma } \varepsilon _{abcd} (\partial _{\mu }\varphi _a)(\partial _{\nu }\varphi _b) (\partial _{\rho }\varphi _c) (\partial _{\sigma }\varphi _d)$ . With the help of a dilaton field $\phi$ we construct theories that are globally scale invariant. In particular, by introducing couplings of the dilaton $\phi$ to the Gauss–Bonnet (GB) topological density $\, {\sqrt{-g}} \, \phi \left( R_{\mu \nu \rho \sigma }^2 - 4 R_{\mu \nu }^2 + R^2 \right) \,$ we obtain a theory that is scale invariant up to a total divergence. Integration of the $\varphi _a$ 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.