Diffusion of Cosmic Rays in Expanding Universe. (I)
  We present an analytic solution to diffusion equation for high energy cosmic rays in the expanding universe. The particles are assumed to be ultra-relativistic and they can have energy losses arbitrarily dependent on energy and time. The obtained solution generalizes the Syrovatsky solution, valid for the case when energy losses and diffusion coefficient are time-independent. 
V. Berezinsky and A. Z. Gazizov