Quantum cosmological backreactions. I. Cosmological space adiabatic perturbation theory

Quantum cosmology, including quantum cosmological inhomogeneities, is a promising framework for describing the very early universe in which all degrees of freedom are being considered as dynamical and quantum. However, many previous discussions on this subject consider perturbations test fields curved spacetime with effective modifications thus neglect certain interactions subsystems, namely backreaction inhomogeneous background. In series four papers, first, we aim at improving treatment effects that arise due to backreactions between matter geometry well homogeneous freedom. We employ technique space adiabatic perturbation theory form developed by Panati, Spohn, Teufel relies familiar Born-Oppenheimer approximation. extend scheme field perturbative setting show leads presently neglected correction terms Friedmann equations. first article, provide detailed introduction iterative examine generic challenges encountered its application cosmology. Our results will allow direct comparison observations.