Fluctuation-dissipation theorems in an expanding universe

The recently constructed minimal extension of the special relativistic Ornstein-Uhlenbeck process to curved space-time cannot be used to model realistically diffusions on cosmological scales because it does not take into account the evolution of the thermodynamical state of the matter with cosmological time. We therefore introduce a new class of non-minimal extensions characterized by time-dependent friction and noise coefficients. These new processes admit time-dependent Juttner distributions as possible measures in momentum space; associated fluctuation-dissipation theorems are also proved and discussed. (c) 2007 American Institute of Physics.