Chiral phase transition with primordial black holes: Distinct phase structure and catalysis

We study the impact of primordial black holes (PBHs) on the chiral phase transition and its associated stochastic gravitational-wave (GW) signals. Using the three-flavor Nambu-Jona-Lasinio model, we construct the chiral effective potential in a Schwarzschild spacetime background. We find that PBHs promote chiral symmetry restoration and induce a nontrivial local phase structure in the vicinity of the event horizon simultaneously. In particular, this structure exhibits a novel chiral symmetry breaking pattern involving both second- and first-order phase transitions, a feature absent in flat spacetime. We further demonstrate that PBHs act as genuine catalysts for the chiral phase transition by analyzing the bounce solution in curved spacetime. The presence of PBHs substantially enhances the inverse duration parameter $β/H$ while leaving the overall transition strength comparable to that in flat spacetime. As a consequence, even a small population of PBHs can induce $\mathcal{O}(1)$ shifts in both the peak frequency and the peak amplitude of the GW spectrum generated by the first-order dark chiral phase transition.

💡 Research Summary

This paper investigates the profound impact of Primordial Black Holes (PBHs) on the chiral phase transition and the associated stochastic gravitational-wave (GW) background. The authors employ the three-flavor Nambu-Jona-Lasinio (NJL) model as an effective framework to describe chiral symmetry breaking and its restoration. They rigorously construct the finite-temperature effective potential within a general curved spacetime background, specifically applying it to the Schwarzschild geometry surrounding an isolated PBH.

The core finding is that PBHs do not merely serve as a passive gravitational background but actively reshape the phase transition dynamics. Near the PBH event horizon, spacetime curvature induces significant corrections to the effective potential. This leads to a novel local phase structure absent in flat spacetime: as the temperature decreases, the system undergoes a sequence of a second-order phase transition, followed by a first-order transition, and finally restores chiral symmetry in the immediate vicinity of the horizon. This demonstrates that PBHs promote local chiral symmetry restoration while creating a complex, inhomogeneous phase diagram.

Furthermore, the study quantitatively establishes PBHs as genuine catalysts for the phase transition. By computing the bounce solution (critical bubble profile) in the curved spacetime, the authors extract key transition parameters: the transition strength (α) and the inverse duration (β/H). They find that the presence of PBHs substantially enhances β/H (accelerating the transition) while leaving α largely unchanged. This catalytic effect means the phase transition completes more rapidly in regions influenced by PBHs.

This modified dynamics has direct observational consequences for the generated GW spectrum. The catalyzed transition predicts a GW signal with a higher peak frequency and a lower peak amplitude compared to the standard flat-space case. Crucially, even a minuscule cosmological abundance of PBHs (f_PBH) can induce order-one shifts in these spectral features. The paper provides concrete examples of how these shifted spectra could fall within the sensitivity bands of future GW observatories like LISA (in the milli-Hz range) and pulsar timing arrays like NANOGrav (in the nano-Hz range).

In summary, the work provides a novel framework for analyzing non-perturbative quantum phenomena, like chiral symmetry breaking, in strong gravitational fields. It reveals that PBHs can dramatically alter the phase transition landscape, acting as local catalysts, and thereby imprinting distinct signatures on the stochastic GW background, with significant implications for probing both particle physics models and the population of PBHs in the early universe.