Backreaction effects and Initial conditions in Quantum Cosmology
The aim of my research project is to start the construction of the Quantum Cosmology sector of Loop Quantum Gravity. In contrast to the already established theory of Loop Quantum Cosmology, which is not derived as a symmetry-reduced version of Loop Quantum Gravity, but which represents an independent theory, the project attempts to deduce and to understand the true cosmological part of Loop Quantum Gravity.
Backreaction effects of matter on geometry and the quantum nature of geometry will be faced squarely. The approach taken in this thesis will be based on a new Hilbert space representation with direct integral structure underlying the Born-Oppenheimer-Approximation. Indeed, such a representation is well adapted to cosmological situations where matter and geometry are treated at different mass scales.
In this framework, I will work with a manifestly gauge invariant scheme by using suitable material reference systems. The approach is ideally suited in order to shed new light on questions about the predictive power of Quantum Cosmology in general and to understand how quantum effects of gravity propagate during the evolution of the universe. The project has the advantageous perspective to be compared directly to recent cosmological observations.