# Small dark energy and stable vacuum from Dilaton-Gauss-Bonnet coupling in TMT Academic Article

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### 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.

### publication date

• April 13, 2017