Duality and the cosmological constant

Abstract

A dynamical theory is studied in which a scalar field $ϕ$ in Einstein- Minkowski space is coupled to the four-velocity $N_μ$ of a preferred inertial observer in that space. As a consistent requirement on this coupling we study a principle of duality invariance of the dynamical mass- term of $ϕ$ at some universal length in the small-distance regime. In the large-distance regime duality breaking can be introduced by giving a back- ground value to $ϕ$ and a back-ground direction to $N_μ$. It is shown that, in an appropriate approximation, duality breaking can be related to the emergence of a characteristic phase in which the condensation of the ground state allows massive excitations with a characteristic scale of squared mass which agrees with present observational bound for the cosmological constant.