Quark-Hadron Phase Transitions in Viscous Early Universe

TL;DR

This paper investigates the quark-hadron phase transition in the early universe, incorporating bulk viscosity effects, analyzing the evolution of key cosmological parameters through analytical and numerical methods, and comparing first-order and crossover transition scenarios.

Contribution

It provides a systematic study of viscous effects on the quark-hadron phase transition, including both first-order and crossover models, with detailed numerical estimations of cosmological evolution.

Findings

Viscous effects significantly influence the evolution of the early universe during the QCD phase transition.

Numerical results show distinct behaviors of the scale factor and Hubble parameter across different transition phases.

The study compares first-order and crossover transition models, highlighting their impact on cosmological parameters.

Abstract

Based on hot big bang theory, the cosmological matter is conjectured to undergo QCD phase transition(s) to hadrons, when the universe was about $1-10 \mu$s old. In the present work, we study the quark-hadron phase transition, by taking into account the effect of the bulk viscosity. We analyze the evolution of the quantities relevant for the physical description of the early universe, namely, the energy density $\rho$, temperature $T$, Hubble parameter $H$ and scale factor $a$ before, during and after the phase transition. To study the cosmological dynamics and the time evolution we use both analytical and numerical methods. By assuming that the phase transition may be described by an effective nucleation theory (prompt {\it first-order} phase transition), we also consider the case where the universe evolved through a mixed phase with a small initial supercooling and monotonically growing hadronic bubbles. The numerical estimation of the cosmological parameters, $a$ and $H$ for instance, makes it clear that the time evolution varies from phase to phase. As the QCD era turns to be fairly accessible in the high-energy experiments and the lattice QCD simulations, the QCD equation of state is very well defined. In light of this, we introduce a systematic study of the {\it cross-over} quark-hadron phase transition and an estimation for the time evolution of Hubble parameter.