4.
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 background value to ϕ and a background 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 the present observational bound for the cosmological constant.
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