  This article reviews some aspects of local covariance and of the ambiguities
and anomalies involved in the definition of the stress energy tensor of quantum
field theory in curved spacetime. Then, a summary is given of the approach
proposed by Buchholz et al. to define local thermal equilibrium states in
quantum field theory, i.e., non-equilibrium states to which, locally, one can
assign thermal parameters, such as temperature or thermal stress-energy. The
extension of that concept to curved spacetime is discussed and some related
results are presented. Finally, the recent approach to cosmology by Dappiaggi,
Fredenhagen and Pinamonti, based on a distinguished fixing of the stress-energy
renormalization ambiguity in the setting of the semiclassical Einstein
equations, is briefly described. The concept of local thermal equilibrium
states is then applied, to yield the result that the temperature behaviour of a
quantized, massless, conformally coupled linear scalar field at early
cosmological times is more singular than that of classical radiation.
