Majoron Dark Energy via Freezing Induced by Quantum Coherence

Abstract

We propose a nonequilibrium mechanism for Majoron dark energy in which the late-time freezing of a physical Majoron is induced by quantum coherence in a hidden pseudo-Dirac sterile fermion reservoir. The evolving Majoron background derivatively couples to the hidden pseudo-Dirac number current and drives a lagged reservoir response with a finite memory time. In the short-memory regime, the causal response kernel reduces to \(\dot X+Γ_{\rm PD}X=β\ddotϕ\). The leading linear-response matching \(Q=αX\) then yields an effective scalar equation containing the exchange structure \(q_{\rm exch}\ddotϕ/\dotϕ\). We show that this term can dynamically suppress the Majoron velocity and sustain a response-dominated freezing branch even when the intrinsic Majoron mass is larger than the present Hubble scale. The microscopic origin of the lag variable is identified with the phase-lagged off-diagonal coherence of the hidden pseudo-Dirac ensemble, while the response strength is controlled by a response-weighted hidden density rather than by an independent gravitating component. The resulting state is a metastable nonequilibrium frozen phase with \(w_ϕ\simeq -1\), rather than an exactly static cosmological constant.