Thermal Green functions in an expanding universe

We examine the problem of formulating thermal Green functions for conformally non-invariant field theories in an FRW cosmology. In contrast to the conformally invariant case, the problem is one in non-equilibrium thermodynamics. Our method which involves choosing an appropriate density matrix leads to a version of the imaginary time formalism. The results make contact with elementary relativistic kinetic theory. Renormalisation is discussed in low order and a running coupling constant dependent on the cosmological scale emerges naturally as an expansion parameter. (orig.)