this contribution is the concept of local thermal equilibrium states and their properties in quantum field theory on cosmological spacetimes. The starting point for our considerations is the notion of local covariant quatum field theory which has been developed in [@VerSPST; @BFV; @HolWald] and which is also reviewed in [@BGP] and is, furthermore, discussed in Chris Fewster’s contribution to these conference proceedings [@cjfgm]. I will therefore attempt to be as much as possible consistent with Fewster’s notation and shall at several points refer to his contribution for precise definitions and further discussion of matters related to local covariant quantum field theory.

The basic idea of local covariant quantum field theory is to consider not just a quantum field on some fixed spacetime, but simultaneously the “same” type of quantum field theory on all — sufficiently nice — spacetimes at once. In making this more precise, one collects all spacetimes which one wants to consider in a category [Loc]{}. By definition, an object in [Loc]{} is a four-dimensional, globally hyperbolic spacetime with chosen orientation and time-orientation. An arrow, or morphism of $\boldsymbol{M} \overset{\psi}{\longrightarrow} \boldsymbol{N}$ of [Loc]{} is an isometric, hyperbolic embedding which preserves orientation and time-orientation. (See Fewster’s contribution for more 