Assessing the role of the Kelvin-Helmholtz instability at the QCD cosmological phase transition

TL;DR

This study uses numerical simulations to investigate how Kelvin-Helmholtz instability could have amplified turbulence and gravitational waves during the QCD phase transition in the early universe, highlighting non-linear effects at higher Mach numbers.

Contribution

It provides the first detailed numerical analysis of Kelvin-Helmholtz instability behavior during the QCD transition using realistic equations of state and explores its potential cosmological implications.

Findings

Kelvin-Helmholtz instability can significantly amplify turbulence in primordial plasma.

Non-linear effects become important at Mach numbers above 0.1.

Instability may increase primordial gravitational radiation.

Abstract

We performed numerical simulations with the PLUTO code in order to analyze the non-linear behavior of the Kelvin-Helmholtz instability in non-magnetized relativistic fluids. The relevance of the instability at the cosmological QCD phase transition was explored using an equation of state based on lattice QCD results with the addition of leptons. The results of the simulations were compared with the theoretical predictions of the linearized theory. For small Mach numbers up to $M_s \sim 0.1$ we find that both results are in good agreement. However, for higher Mach numbers, non-linear effects are significant. In particular, many initial conditions that look stable according to the linear analysis are shown to be unstable according to the full calculation. Since according to lattice calculations the cosmological QCD transition is a smooth crossover, violent fluid motions are not expected. Thus, in order to assess the role of the Kelvin-Helmholtz instability at the QCD epoch, we focus on simulations with low shear velocity and use monochromatic as well as random perturbations to trigger the instability. We find that the Kelvin-Helmholtz instability can strongly amplify turbulence in the primordial plasma and as a consequence it may increase the amount of primordial gravitational radiation. Such turbulence may be relevant for the evolution of the Universe at later stages and may have an impact in the stochastic gravitational wave background.