Primordial Tangyuan Quark Stars Made of Longevous False Vacuum

TL;DR

This work demonstrates that metastable false vacuum can persist cosmologically in locally high quark chemical potential regions during a first-order QCD transition, enabling the formation of primordial quark objects. It builds a dynamical phase diagram using a two-flavor quark-meson model, solves gap equations under $\beta$-equilibrium and charge neutrality, and computes bubble-nucleation rates with $\Gamma = T^4 \left(\frac{S_3}{2\pi T}\right)^{\frac{3}{2}} e^{-{S_3}/{T}}$ to identify longevous false vacuum windows (e.g., a red ring near $\mu = 0.30066$ GeV, $T = 0.0204$ GeV where $\tau \sim 10^{10}$ years). Two branches emerge: quark stars crusted with false vacuum and nuggets with global false vacuum; typical quark stars have $R \sim \mathcal{O}(10)$ km and $M \sim \mathcal{O}(M_\odot)$ with FV crusts of $\mathcal{O}(10-100)$ m, while nuggets satisfy $M < 0.015\,M_\odot$ and $R < 2.6$ km. If the false vacuum decays, vacuum energy can reach $E_v \lesssim 10^{54}$ erg for crusts (and potentially $\sim 10^{56}$ erg isotropically via jets), enabling ultra-energetic long GRBs and multi-kHz GW signals, providing testable multi-messenger signatures and implications for early star formation and black hole seeding. The results frame false vacuum decay in cosmological remnants as observable astrophysical phenomena and suggest broader applicability to other supercooled systems and dark-sector scenarios.

Abstract

A false vacuum could be a profound ingredient of fundamental physics, yet its direct detection in laboratories is hindered when the lifetime is exponentially long. Conventional static phase diagrams often discard metastable false vacuum, we show that, however, in a dynamical treatment of a first-order QCD phase transition at large quark chemical potential that strongly suppresses tunneling, cosmologically longevous, and thus indispensable false vacuum naturally arises, and makes nontrivial contribution to constituting primordial quark objects. We identify two distinct branches of such primordial quark objects: quark star crusted with false vacuum, and nugget specifically referring to quark star in global false vacuum, which may account for a population of small compact stars. False vacuum in primordial objects hopefully decays during the long time since the early Universe, and its vacuum energy can power ultra-energetic long γ-ray bursts and kHz gravitational waves within multi-messenger facilities, rendering itself an astrophysical and thus testable phenomenon.

Figures (3)

• Figure 1: The schematic diagram of the potential with high barrier that suppresses the tunneling process of bubble nucleation in a dynamical first-order phase transition.
• Figure 2: The dynamical phase diagram with the temperature $T$ and the quark chemical potential $\mu$. The red boundary line of the red shaded true vacuum quark matter region is the static first-order phase transition line with the critical end point at $\mu=0.2824$ GeV and $T=0.04649$ GeV indicated by the red star. The blue boundary line of the blue shaded hardon region is the spinodal line, below which no false vacuum quark matter can exist. The green boundary line marks the relation $T(\mu)$ for which the total pressure vanishes. The red ring at $\mu=0.30066$ GeV and $T=0.0204$ GeV indicates the vicinity where the lifetime of $1$ km$^3$ false vacuum is around the age of the Universe. The false vacuum (FV for short in the figure) can be longevous in the green shaded region but is ephemeral in the lighter gray region or astrophysically unstable with negative total pressure in the darker gray region.
• Figure 3: The mass-radius relation of quark objects at $T=20.4$ MeV (red) and $T=10$ MeV (blue). The triangles and dashed lines indicate the boundaries between false-vacuum-crusted stars and nuggets, and six schematic diagrams of representative objects are chosen from the red line (black dots). The shaded regions show the observational constraints from various sources (see text for references).