Revisiting QCD-induced little inflation with chiral density wave state and its implications on pulsar timing array gravitational-wave signals

TL;DR

This paper investigates whether a chiral density wave phase at high baryon chemical potential can alter the QCD phase transition's supercooling, affecting gravitational-wave signals relevant for pulsar timing arrays.

Contribution

It analyzes the impact of the chiral density wave phase on QCD phase transition dynamics and gravitational-wave production, providing conditions for their cosmological relevance.

Findings

The chiral density wave phase can be metastable at low baryon densities.

Latent heat released is too small for a viable inflation scenario.

Inhomogeneous QCD phases may influence gravitational-wave signals.

Abstract

We revisit QCD-induced little inflation in which the Universe starts with a large baryon chemical potential and undergoes a strong first-order QCD phase transition, generating an observable stochastic gravitational-wave background in the nano-Hz range relevant for pulsar timing array (PTA) observations. We point out that the conventional homogeneous transition from the quark-gluon plasma phase to the hadronic gas phase faces an unavoidable difficulty in achieving the required strength of supercooling for the observed baryon density. This motivates us to explore whether a qualitatively different phase structure at a large baryon chemical potential can alter the relation between the baryon density and the chemical potential, and thereby modify the supercooling history of the transition. Using the nucleon-meson model with isoscalar vector mesons, we determine the critical and spinodal structure of the chiral density wave (CDW) phase in the $(\mu_B, T)$ plane. We find that the CDW phase exhibits a nontrivial structure and can remain metastable down to a low baryon density in a certain region of the parameter space. Taking into account the subsequent liquid-gas transition and phase separation, however, the released latent heat is too small to realize a viable QCD-induced little inflation scenario and its associated PTA-scale gravitational-wave signal. Our analysis sharpens the conditions under which QCD phase transitions may act as cosmological sources of nano-Hz gravitational waves, while clarifying the possible cosmological relevance of inhomogeneous QCD phases.