Unveiling the cosmological QCD phase transition through the eLISA/NGO
  detector
  We study the evolution of turbulence in the early universe at the QCD epoch
using a state-of-the-art equation of state derived from lattice QCD
simulations. Since the transition is a crossover we assume that temperature and
velocity fluctuations were generated by some event in the previous history of
the Universe and survive until the QCD epoch due to the extremely large
Reynolds number of the primordial fluid. The fluid at the QCD epoch is assumed
to be non-viscous, based on the fact that the viscosity per entropy density of
the quark gluon plasma obtained from heavy-ion collision experiments at the
RHIC and the LHC is extremely small.
  Our hydrodynamic simulations show that the velocity spectrum is very
different from the Kolmogorov power law considered in studies of primordial
turbulence that focus on first order phase transitions. This is due to the fact
that there is no continuous injection of energy in the system and the viscosity
of the fluid is negligible. Thus, as kinetic energy cascades from the larger to
the smaller scales, a large amount of kinetic energy is accumulated at the
smallest scales due to the lack of dissipation.
  We have obtained the spectrum of the gravitational radiation emitted by the
motion of the fluid finding that, if typical velocity and temperature
fluctuations have an amplitude $(\Delta v) /c \gtrsim 10^{-2}$ and/or $\Delta
T/T_c \gtrsim 10^{-3}$, they would be detected by eLISA at frequencies larger
than $\sim 10^{-4}$ Hz.
