Quantum cosmological backreactions. III. Deparametrized quantum cosmological perturbation theory

This is the third paper in a series of four in which we incorporate backreaction among the homogeneous as well as between the homogeneous and inhomogeneous degrees of freedom in quantum cosmological perturbation theory using space adiabatic methods. Here, we consider a gauge-fixed version of cosmological perturbation theory which uses Gaussian dust as a material reference system. The observable matter content is a real-valued scalar field. We explore the sector of that theory which is purely homogeneous and isotropic with respect to the geometry degrees of freedom but which contains inhomogeneous perturbations up to second order of the scalar field. We explore the quantum field theoretical challenges of the space adiabatic framework in a cosmological model of the early universe which is technically still relatively simple. We compute the quantum backreaction effects from the inhomogeneous matter modes on the homogeneous geometry up to second order in the adiabatic parameter. It turns out that these contributions are not negligible.