On the survival of strong nuggets in the early Universe

Abstract

Strong nuggets with a baryon number of $A\sim 10^{10-30}$ could be able to survive from the cosmic separation of the QCD phases, provided the transition from strange quark matter to strangeon matter is accounted for, thereby evading evaporation in the early Universe. Such strangeon nuggets may serve as a dark matter candidate within particle standard model. We formulate the corresponding phase transition of cosmic strange matter, establishing a parameter space which reasonably accommodates observational constraints on the dark-to-luminous matter ratio and the mass-radius relation, as well as tidal deformability of compact objects.

Figures (4)

• Figure 1: Left panel: Pressure $p$ as a function of the baryon chemical potential $\mu_{\rm B}$ for strange quark matter and strangeon matter. The MIT bag model calculations for strange quark matter with $(B^{1/4}=159~\mathrm{MeV}, T=40~\mathrm{MeV})$ and $(B^{1/4}=159~\mathrm{MeV}, T=50~\mathrm{MeV})$ are shown as the solid-green and solid-blue curves, respectively. The dot-dashed curves represent the results for strangeon matter with $(m_1=710~\mathrm{MeV}, m_2=239~\mathrm{MeV}, u_{0}^{(0)}=303~\mathrm{MeV}$, $r_0^{(0)}=2.06~\mathrm{fm})$ at $T=40~\mathrm{MeV}$ and $T=50~\mathrm{MeV}$. Right panel: The strange quark-strangeon phase diagram in the $T–\mu_B$ plane.
• Figure 2: The strange quark nugget temperature at which it loses 15% of its baryon number due to evaporation (we define it as $T_{\rm nug,\,15}$). In the calculation, we assume the strange quark nugget forming temperature $T_{\rm u0} = 100\,{\rm MeV}$, with initial baryon number $A_0$ ranged from $10^7$ to $10^{57}$ and binding energy per baryon $\delta E$ from 0 to $75\;\text{MeV}$.
• Figure 3: Left panel: the parameter space of strangeon EoS in which the corresponding phase transition temperature cause strange quark nugeets to undergo phase transition to strangeon nuggets at a certain $A_0$ and $\delta E$, retaining 85% of its baryon number. The red area contains 90% of the sampled dots. In the calculation, $T_0$ in Eq. (\ref{['eq:T0']}) is set to 100 MeV, at the same level as the QCD phase transition temperature karsch_lattice_2000rajagopal_condensed_2001fukushima_phase_2010. Right panel: the parameter space of strangeon EoS obtained by a Bayesian inference using the mass-radius measurements from NICER, such as PSR J0030+0451 riley_nicer_2019vinciguerra_updated_2024miller_psr_2019, PSR J0437-4715 choudhury_nicer_2024rutherford_constraining_2024, PSR J0740+6620 miller_radius_2021riley_nicer_2021, and the tidal deformability measurement of LIGO/Virgo from GW170817 ligo_observation_2017ligo_gw170817_2018abbott_properties_2019, within the allowed parameter space in the left panel. The contour confidence levels are 50% and 90%.
• Figure 4: The left panel is the mass-radius curves of the strangeon stars calculated through the TOV equations oppenheimer_massive_1939. The right panel is the tidal deformability-mass curves of the strangeon star calculated by the gauge perturbation equations hinderer_tidal_2008. The solid-blue line shows that four EoS parameters are equal to their average value inferred in the right panel of Fig. \ref{['fig:params']}, i.e. $m_1=710\,\;\text{MeV}$, $m_2=239\,\;\text{MeV}$, $u_0^{(0)}=303\,\;\text{MeV}$, $r_0^{(0)}=2.06\,{\rm fm}$. The other four lines each change one of the four parameters. The dashed-orange line represents the change in $m_1$ to $1022\,\;\text{MeV}$. The dotted-green line alters $m_2$ to $337\,\;\text{MeV}$. The dash-dotted-red line turns $u_0^{(0)}$ to $193\,\;\text{MeV}$. The dash-dash-dotted-purple line changes $r_0^{(0)}$ to $2.42\,{\rm fm}$.