Revisiting QCD-induced little inflation with chiral density wave state and its implications on pulsar timing array 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 $(μ_B, T)$ 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.

Figures (9)

• Figure 1: The schematic QCD phase diagram in the $T-\mu_{B}$ plane proposed in this work. CDW, QGP and CFL denote the chiral density wave, quark-gluon plasma and color-flavor locking (color superconducting) phases, respectively.
• Figure 2: Contour plots of the thermodynamic potential $\Omega(T,\mu_B,\phi,q)$ in the $(\phi,q)$ plane for various values of $\mu_B$ and $T=0$, with $M_0=0.81m_N$, $K=250$ MeV, $d=10^4$. The middle and right panels show the emergence of a local minimum at a non-zero $q$. These plots do not depict the potential at $q=0$.
• Figure 3: The reduced effective potential $\Delta \Omega$, defined in Eq. \ref{['eq:reduced_poten']}, as a function of the wave number $q$ for various values of the chemical potential $\mu_B$ at $T = 0$. The other input parameters are fixed to $M_0=0.81m_N$, $K=250\,\mathrm{MeV}$, $d=10^4$.
• Figure 4: Zero-temperature phase structure as a function of the model parameter $M_0$. We fix $K=250$ MeV and use three representative values of $d$ as shown in the legend. The black solid line denotes the baryon onset chemical potential $\mu_0=922.7\,\mathrm{MeV}$ below which $n_B=0$.
• Figure 5: Free-energy difference of the CDW phase with respect to the thermodynamically stable isotropic phase, $\Delta \Omega$ n Eq. \ref{['eq:reduced_poten']}, as a function of temperature $T$ at fixed $\mu_B = 1200$ MeV. The input parameters are fixed to $M_0=0.81m_N$, $K=250$ MeV, and $d=10^4$.