Supercooling and phase coexistence in cosmological phase transitions

TL;DR

Problem: understanding first-order cosmological phase transitions and how supercooling, reheating, and phase coexistence unfold under thermodynamic constraints. Approach: combine general thermodynamic relations with a Higgs-like finite-temperature effective potential to study dynamics and produce numerically solved evolution of temperature, scale factor, and bubble nucleation. Findings: latent heat and radiation density bound the duration and stage structure; phase coexistence occurs under certain L vs delta rho_R conditions and is more likely at lower energy scales or with fewer degrees of freedom; cosmological implications include constraints on late-time dark-energy models and effects on electroweak baryogenesis, baryon inhomogeneities, topological defects, and primordial magnetic fields. Significance: provides model-independent thermodynamic criteria and a practical framework for predicting outcomes of cosmological first-order transitions across a range of theories.

Abstract

Cosmological phase transitions are predicted by Particle Physics models, and have a variety of important cosmological consequences, which depend strongly on the dynamics of the transition. In this work we investigate in detail the general features of the development of a first-order phase transition. We find thermodynamical constraints on some quantities that determine the dynamics, namely, the latent heat, the radiation energy density and the false-vacuum energy density. Using a simple model with a Higgs field, we study numerically the amount and duration of supercooling and the subsequent reheating and phase coexistence. We analyze the dependence of the dynamics on the different parameters of the model, namely, the energy scale, the number of degrees of freedom and the couplings of the scalar field with bosons and fermions. We also inspect the implications for the cosmological outcomes of the phase transition.

Figures (10)

• Figure 1: Contours of constant time in the allowed region of the plane $(\rho _{\Lambda }/\rho _{R}$,$L/\rho _{R})$. From bottom to top, the curves correspond to $\Delta t/\tilde{t}=0.2,0.5,1,2,3$ and $5$. The points correspond to varying $h_b$ in the model of section \ref{['themodel']} for $h_f=0.7$ (blue squares), $h_f=h_b$ (black triangles), and $h_f=h_b$ with $\mu_b\neq 0$ (red circles). The three curves on the right correspond to $g_l=0$, and those on the left to $g_l/g_*\approx 0.44$.
• Figure 2: The free energy around $T=T_c$.
• Figure 3: The effective potential at $T=T_c$. Left: $h_f=0.7$. Right: $h_f=h_b$. The numbers next to the curves indicate the corresponding values of $T_c/v$.
• Figure 4: The temperature variation for the potential of Fig. \ref{['pot']}.
• Figure 5: Temperature variation for $g_l=30$. The three solid lines correspond to $v=246GeV$ and, from right to left, to $\tilde{\eta}=50$, $\tilde{\eta}=5$, and $\tilde{\eta}=0.5$. The dashed lines correspond to $\tilde{\eta} =5$ and, from right to left, to $v=100MeV$ and $v=10^{-3}eV$.