Duality and the cosmological constant

TL;DR

This paper explores a scalar field theory coupled to a preferred observer's velocity in Einstein-Minkowski space, linking duality invariance and breaking to the emergence of a cosmological constant consistent with observations.

Contribution

It introduces a duality-invariant scalar field model that, when broken, naturally leads to a cosmological constant matching current observational bounds.

Findings

Duality invariance constrains the scalar field dynamics.

Breaking duality introduces a ground state with a characteristic phase.

The model predicts a mass scale compatible with the observed cosmological constant.

Abstract

A dynamical theory is studied in which a scalar field $\phi$ in Einstein- Minkowski space is coupled to the four-velocity $N_{\mu}$ 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 $\phi$ 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 $\phi$ and a back-ground direction to $N_{\mu}$. 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.