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.