DFG-NSF: investigations on physical implications of canonical quantum gravity

点击翻译按钮获取中文摘要

The unification of quantum mechanics and general relativity is one of the main fundamental problems of theoretical physics. But, the marriage of quantum and gravity faces many challenging hurdles. In the canonical approaches to quantum gravity, such as loop quantum gravity, the main open problems are to formulate the quantum dynamics in form of so called quantum Einstein equations, along with how does the quantization procedure affects the dynamics, and hence physical implications. All models based on canonical quantum gravity, including loop quantum cosmology which has successfully led to resolution of various singularities and predicts potential signatures in the cosmic microwave background, face above problems in one form or another to yield a reliable physical picture. The main goal of this proposal is to address and gain insights on these fundamental issues using the relational formalism based on clocks and Dirac observables that allows to define gauge invariant quantities in the context of general relativity. Using already existing models for the quantum Einstein equations and results in canonical cosmological perturbation theory, this proposal aims to explore ramifications of these methods in the cosmological setting, both at classical and quantum level, including implications for cosmological perturbation theory. Results from this research on the one hand will test so far available predictions in quantum cosmological models in a more general setting which is closer to full loop quantum gravity, and on the other hand yield valuable insights on the way quantization choices and gauge fixing affect physical predictions.