Inflationary QCD phase diagram

TL;DR

The paper addresses whether inflation can probe QCD-like phase structure by introducing a rolling inflaton that generates an axial chemical potential $μ_5$. It uses the Nambu-Jona-Lasinio model in a de Sitter background and a mean-field treatment to compute the effective potential $V_{eff}$ and solve the gap equations for the chiral condensates. The authors map the phase diagram in the plane $(μ_5/Λ, H/Λ)$, finding a first-order chiral phase transition line and a critical point that appears when $μ_5/Λ$ is sufficiently large and depends on the light-quark mass $m_l$, with the KMT coupling $G_{KMT}$ affecting the line only weakly. This work provides a cosmological collider analogue of the QCD phase diagram, highlighting how inflationary dynamics (through $H$ and $μ_5$) may imprint phase-structure signals, though the conclusions rely on an effective NJL description and regularization choices.

Abstract

Motivated by the cosmological collider program, which aims to probe high-energy physics through inflation, we investigate the phase diagram of multi-flavor QCD in de Sitter spacetime with a flavor-universal axial chemical potential induced by a rolling inflaton coupled to fermions. We determine the first-order critical line and a critical point as functions of the Hubble parameter and the axial chemical potential, employing an effective description of chiral symmetry breaking within the framework of the Nambu--Jona-Lasinio model. We find that a first-order chiral phase transition may occur during inflation or at its end when the axial chemical potential is sufficiently large and crosses the critical line. This provides a cosmological collider analogue of the QCD phase diagram explored in heavy-ion colliders.

Figures (2)

• Figure 1: Inflationary QCD phase diagram is shown on $(\mu_5/\Lambda,H/\Lambda)$-plane, where $H,~\mu_5$ and $\Lambda$ are the Hubble parameter, the inflaton induced axial chemical potential and three dimensional sharp cutoff, respectively. The black solid curve and the blue dashed curve are first-order critical lines, while large points represent critical points for each cases with non-vanishing light fermion masses. The solid orange curve (the case (i)) and purple curve (the case (ii)) represent the first-order critical line, and dotted curves correspond to the second-order critical curves for vanishing light fermion masses.
• Figure 2: Dependence of the effective potential with a fixed $\Sigma_s/\Sigma_{s0}=0.913$ (left) and chiral condensates on the Hubble parameter (right) are shown. In both panels, an axial chemical potential is taken for $\mu_5/\Lambda=0.871$. Chiral condensates $\Sigma_l$ and $\Sigma_s$ are normalized by values at $H/\Lambda=0.185$, where two degenerate potential minima exist.