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Fluctuation-dissipation theorems in an expanding universe. (English) Zbl 1121.82029
Summary: 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 Jüttner distributions as possible measures in momentum space; associated fluctuation-dissipation theorems are also proved and discussed.

MSC:
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
60H30 Applications of stochastic analysis (to PDEs, etc.)
83F05 Relativistic cosmology
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