Shadow vacuum alignment and dark energy

Abstract

In a recent model of dark energy (with several phenomenological consequences), the universe is assumed to be trapped in a false vacuum with an energy density of the order of (10^{-3} eV)^4, mimicking the presently successful $\Lambda CDM$ scenario. This involves a new gauge group SU(2)_Z, {\em the shadow sector}, which becomes strong at a scale $\Lambda_Z \sim 10^{-3} eV$. The model is described by the SU(2)_Z instanton-induced potential of an axion-like scalar field, a_Z, with two degenerate vacuua. The false (metastable) vacuum appears as a result of an phenomenological (ad-hoc) soft breaking term linear in a_Z which explicitely breaks that degeneracy. In this paper, we discuss a possible dynamical origin for this soft breaking term as coming from the alignment of the vacuum along a direction in which the condensate of the shadow fermions, $<\bar{\psi}^{(Z)}_{i} i \gamma_{5} \psi^{(Z)}_{i}>$ which breaks spontaneously both P and CP, is non-vanishing. The present universe lives in a vacuum which violates both P and CP in the shadow SU(2)_Z sector!