Feynman rules for finite-temperature Green’s functions in an expanding universe

We derive Feynman rules for evaluating the real-time Green's functions of a scalar field theory in a Robertson-Walker universe under the circumstance that at some initial time t₀ the system was in thermal equilibrium with density matrix exp[-{β}H(t₀)], where H(t₀) is the Hamiltonian at time t₀.