Field-theoretic dynamics of the CDW wave-number order parameter for nucleation calculations

Determine an effective field-theoretic description for the chiral density wave wave-number order parameter q in the nucleon–meson model with isoscalar vector mesons, including appropriate kinetic and gradient terms, so that bubble nucleation rates for the first-order transition from the chiral density wave phase to the homogeneous hadronic phase can be computed in a cosmological setting.

Background

In the analysis of supercooling and phase transitions between the chiral density wave (CDW) phase and the homogeneous hadronic phase, the authors avoid computing bubble nucleation rates and instead focus on spinodal lines. They explicitly state that this is because the order parameter q (the CDW wave number) lacks a known field-theoretic treatment needed to model spatially varying configurations and compute bounce actions.

A concrete, dynamical field description for q would enable evaluation of nucleation rates, which is crucial for assessing whether supercooling could be sufficiently strong to realize a QCD-induced little inflationary scenario.