Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions

We develop a macroscopic description of the space-time evolution of the energy-momentum tensor during the pre-equilibrium stage of a high-energy heavy-ion collision. Based on a weak coupling effective kinetic description of the microscopic equilibration process (a la bottom-up), we calculate the nonequilibrium evolution of the local background energy-momentum tensor as well as the nonequilibrium linear response to transverse energy and momentum perturbations for realistic boost-invariant initial conditions for heavy-ion collisions. We demonstrate how this framework can be used on an event-by-event basis to propagate the energy-momentum tensor from far-from-equilibrium initial-state models to the time tau(hydro) when the system is well described by relativistic viscous hydrodynamics. The subsequent hydrodynamic evolution becomes essentially independent of the hydrodynamic initialization time tau(hydro) as long as tau(hydro) is chosen in an appropriate range where both kinetic and hydrodynamic descriptions overlap. We find that for root s(NN) = 2.76 TeV central Pb-Pb collisions, the typical timescale when viscous hydrodynamics with shear viscosity over entropy ratio eta/s= 0.16 becomes applicable is tau(hydro) similar to 1 fm/c after the collision.