Collective modes and instabilities in anisotropically expanding ultrarelativistic plasmas

Abstract

The time evolution of collective modes in an expanding ultrarelativistic and (effectively) Abelian plasma is studied in the hard-loop approximation semianalytically by means of integrodifferential equations. A previous treatment is generalized to arbitrary orientation of wave vectors with respect to the direction of anisotropy and thus to a fully $3+1$ dimensional situation. Moreover, initial fluctuations are allowed in both gauge fields and currents, which is necessary in the case of (stable) longitudinal modes. For unstable (Weibel) modes, this generalization of initial conditions reduces drastically the lower bound on the delay in the onset of growth that was found previously by considering only collective gauge fields as seeds. This makes it appear much more likely that non-Abelian plasma instabilities seeded by small initial rapidity fluctuations could play an important role in the early stage of heavy-ion collisions at LHC energies.