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-velocityN _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 background value to ϕ and a background direction toN _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 the present observational bound for the cosmological constant.