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
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
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 
in four dimensions defined in terms of scalars 
by 
. With the help of a dilaton field 
we construct theories that are globally scale invariant. In particular, by introducing couplings of the dilaton to the Gauss–Bonnet (GB) topological density 
we obtain a theory that is scale invariant up to a total divergence. Integration of the 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.
© The Author(s), 2017
