Quantum cosmological backreactions. IV. Constrained quantum cosmological perturbation theory

This is the fourth paper in a series of four which we use space adiabatic methods order to incorporate backreactions among homogeneous and between inhomogeneous degrees freedom quantum cosmological perturbation theory. In this paper, finally consider gauge invariant scalar (Mukhanov-Sasaki) tensor (primordial gravitational wave) perturbations General Relativity coupled an inflaton field arise from careful constraint analysis system up second perturbations. The simultaneous quantisation suggests theory as approximation scheme capture backreaction effects these two sets freedom. We are confronted with all challenges at once that found simpler models treated papers. able compute parameter find significant modifications compared earlier derivations effective dynamics sector.