Approximate KMS states for scalar and spinor fields in Friedmann-Robertson-Walker spacetimes

We construct and discuss Hadamard states for both scalar and Dirac spinor fields in a large class of spatially flat Friedmann\u2013Robertson\u2013 Walker spacetimes characterised by an initial phase either of exponential or of power-law expansion. The states we obtain can be interpreted as being in thermal equilibrium at the time when the scale factor a has a specific value a = a0. In the case a0 = 0, these states fulfil a strict KMS condition on the boundary of the spacetime, which is either a cosmologi- cal horizon or a Big Bang hypersurface. Furthermore, in the conformally invariant case, they are conformal KMS states on the full spacetime. How- ever, they provide a natural notion of an approximate KMS state also in the remaining cases, especially for massive fields. On the technical side, our results are based on a bulk-to-boundary reconstruction tech- nique already successfully applied in the scalar case and here proven to be suitable also for spinor fields. The potential applications of the states we find range over a broad spectrum, but they appear to be suited to discuss in particular thermal phenomena such as the cosmic neutrino background or the quantum state of dark matter