General form of the renormalized, perturbed energy density via
  interacting quantum fields in cosmological spacetimes
  A covariant description of quantum matter fields in the early universe
underpins models for the origin of species, e.g. baryogenesis and dark matter
production. In nearly all cases the relevant cosmological observables are
computed in a general approximation, via the standard irreducible
representations found in the operator formalism of particle physics, where
intricacies related to a renormalized stress-energy tensor in a non-stationary
spacetime are ignored. Models of the early universe also include a dense
environment of quantum fields where far-from-equilibrium interactions manifest
expressions for observables with substantive corrections to the leading terms.
An alternate treatment of these cosmological observables may be carried out
within the framework of algebraic quantum field theory in curved spacetime,
where the field theoretic model of quantum matter is compatible with the
classical effects of general relativity. Here, we take the first step towards
computing such an observable. We employ the algebraic formalism while
considering far-from-equilibrium interactions in a dense environment under the
influence of a classical, yet non-stationary, spacetime to derive an expression
for the perturbed energy density as a component of the renormalized
stress-energy tensor associated with common proposals for quantum matter
production in the early universe.
