Large Scale Inhomogeneities from the QCD Phase Transition

TL;DR

The paper investigates the cosmological QCD phase transition as a first-order process across a wide range of latent heat L and surface tension σ, using the bag equation of state and classical nucleation theory. It demonstrates that significant supercooling can produce large bubble separations l_n, with bubbles growing as detonations or deflagrations and potentially without reheating to Tc. Incorporating a more realistic equation of state with a large heat capacity shows l_n can increase further, depending on the height of the energy-density slope. Regarding nucleosynthesis, detonations appear ineffective at creating baryon inhomogeneities large enough to matter, while deflagrations with strong turbulent transport or neutrino-energy flux could generate observable effects in a narrow region of parameter space. The authors highlight the critical role of the QCD equation of state and call for lattice QCD inputs to refine these predictions.

Abstract

We examine the first-order cosmological QCD phase transition for a large class of parameter values, previously considered unlikely. We find that the hadron bubbles can nucleate at very large distance scales, they can grow as detonations as well as deflagrations, and that the phase transition may be completed without reheating to the critical temperature. For a subset of the parameter values studied, the inhomogeneities generated at the QCD phase transition might have a noticeable effect on nucleosynthesis.

Figures (6)

• Figure 1: The supercooling $1-\hat{T}_f$ and the bubble distance scale $l_n$. The distance scale is given as $l_n/vt_H$, where $t_H$ is the Hubble distance ("horizon") and $v$ is the detonation or shock velocity, $1/{\sqrt3} < v < 1$. The dependence on the surface tension $\sigma$ and the latent heat $L$ is through the combination $\sigma^3/L^2T_c$. We also show the nucleation action $S(t_f)$. The other thin lines show the two quantities $S"(t_f)/S'(t_f)^2$ (short-dashed line) and $\bigl[|S'(t_f)|(t_f-t_c)\bigr]^{-1}$ (dotted line), whose smallness we have assumed. Our approximations are seen to break down at $\sigma^3/L^2T_c \hbox{$\,$$>$ $\sim$$\,$} 0.25$.
• Figure 2: Contours of the critical radius $r_c$ and the bubble separation $l_n$ on the $(L,\sigma)$ parameter plane. The solid line corresponds to $\sigma^3/L^2T_c = 0.25$. This figure is for the bag equation of state. equation of As discussed in the text, use of a more realistic equation of state could increase the distances $l_n$ by an order of magnitude or more.
• Figure 3: Schematic representation of the energy density versus $T^4$ for three different equations of state. Thinner parts of the curves denote the metastable branches. For clarity the magnitude of $L$ has been exaggerated in the figure.
• Figure 4: Detonations and deflagrations: This plot shows how the different processes lie in the $(\epsilon_h,\epsilon_q)$-plane. The entropy condition restricts the allowed processes below the $\Delta S = 0$ curve. Point C corresponds to $T_q = T_h = T_c$. For a given $T_f$ there is a 1-dimensional family of solutions, denoted by the dashed line. The detonation branch of this family is a horizontal line, the deflagration branch a steep curve. For any $T_f<T_c$ it always passes to the left of point C, indicating that weak deflagrations are allowed. If it passes to the left of G, strong deflagrations are allowed. If the detonation branch passes below D (J), then weak (Jouguet) detonations are allowed. This figure is for $r = 1.01$.
• Figure 5: Some special temperatures for the bag equation of state as a function of $r$. $T_q({\rm D})$ is the maximum temperature for which (weak) detonations are allowed. $T_q({\rm J})$ is the maximum temperature for which Jouguet detonations are allowed. $T_f({\rm G})$ is the maximum temperature for which Jouguet deflagrations are allowed. For $T<T_f({\rm G})$, strong deflagrations are allowed. $T_r$ is the lowest temperature for which the latent heat is sufficient to reheat the universe back to $T_c$.