Local covariance, renormalization ambiguity, and local thermal equilibrium in cosmology

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.