Synchrotron signature of a relativistic blast wave with decaying
  microturbulence
  Microphysics of weakly magnetized relativistic collisionless shock waves,
corroborated by recent high performance numerical simulations, indicate the
presence of a microturbulent layer of large magnetic field strength behind the
shock front, which must decay beyond some hundreds of skin depths. The present
paper discusses the dynamics of such microturbulence, borrowing from these same
numerical simulations, and calculates the synchrotron signature of a powerlaw
of shock accelerated particles. The decaying microturbulent layer is found to
leave distinct signatures in the spectro-temporal evolution of the spectrum
$F_\nu \propto t^{-\alpha}\nu^{-\beta}$ of a decelerating blast wave, which are
potentially visible in early multi-wavelength follow-up observations of
gamma-ray bursts. This paper also discusses the influence of the evolving
microturbulence on the acceleration process, with particular emphasis on the
maximal energy of synchrotron afterglow photons, which falls in the GeV range
for standard gamma-ray burst parameters. Finally, this paper argues that the
evolving microturbulence plays a key role in shaping the spectra of recently
observed gamma-ray bursts with extended GeV emission, such as GRB090510.
