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

September 27, 2010

We construct and discuss Hadamard states for both scalar and Dirac spinor
fields in a large class of spatially flat Friedmann-Robertson-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=a_0. In
the case a_0=0, these states fulfil a strict KMS condition on the boundary of
the spacetime, which is either a cosmological horizon, or a Big Bang
hypersurface. Furthermore, in the conformally invariant case, they are
conformal KMS states on the full spacetime. However, 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 technique 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.

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