Localized (Super)Gravity and Cosmological Constant

TL;DR

This paper explores how gravity can be localized on non-singular domain walls in Einstein-scalar theories, showing conditions for stable solutions with infinite tension and analyzing implications for the cosmological constant and higher curvature effects.

Contribution

It demonstrates the existence of stable, non-singular domain wall solutions with infinite tension and discusses their implications for gravity localization and the cosmological constant.

Findings

Non-singular domain walls with infinite tension can localize gravity.

Higher derivative terms do not affect the vanishing cosmological constant.

Higher curvature terms can delocalize gravity, affecting Newton's law.

Abstract

We consider localization of gravity in domain wall solutions of Einstein's gravity coupled to a scalar field with a generic potential. We discuss conditions on the scalar potential such that domain wall solutions are non-singular. Such solutions even exist for appropriate potentials which have no minima at all and are unbounded below. Domain walls of this type have infinite tension, while usual kink type of solutions interpolating between two AdS minima have finite tension. Non-singular domain walls with infinite tension might a priori avoid recent ``no-go'' theorems indicating impossibility of supersymmetric embedding of kink type of domain walls in gauged supergravity. We argue that (non-singular) domain walls are stable even if they have infinite tension. This is essentially due to the fact that localization of gravity in smooth domain walls is a Higgs mechanism corresponding to a spontaneous breakdown of translational invariance. We point out that if the scalar potential has no minima and approaches finite negative values at infinity, then higher derivative terms are under control, and do not affect the cosmological constant on the brane which is vanishing for such backgrounds. Nonetheless, we also point out that higher curvature terms generically delocalize gravity, so that the desired lower dimensional Newton's law is no longer reproduced.