  A quasi-particle model is employed to derive from available lattice QCD
calculations an equation of state useable in hydrodynamical simulations of the
expansion stage of strongly interacting matter created in ultra-relativistic
heavy-ion collisions. Various lattice results give an astonishing agreement of
the pressure as a function of energy density at large energy densities supposed
the pseudo-critical temperature is in the range $170 \pm 15$ MeV, while in the
transition region the equation of state is not yet well constrained. Therefore,
one can construct a family of equations of state by bridging the uncertain
region from the uniquely given high-energy density region part to a hadronic
equation of state by suitable interpolation together with the extrapolation to
non-zero baryon density by means of the quasi-particle model. We present a
series of tests of the model, discuss the chiral extrapolation and the role of
Landau damping. We also briefly sketch the path of cosmic matter in the early
universe in the phase diagram.
