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