Effective Descriptions of Quantum Gravity and Cosmology

The main aim of this project is to complete the formulation of effective descriptions of quantum systems in canonical language. Especially the field of canonical quantum gravity (including loop quantum gravity) requires a more general setting than standard effective actions, allowing for instance for an enlarged gauge structure, general covariance and the associated freedom to change the time variable, and a non-Gaussian or non-vacuum state as expansion basis. Compared to existing formulations, the major extension provided by work in the project will lead to a canonical version of effective quantum field theory. Applications will include an analysis of renormalization in canonical quantum gravity, comparisons with existing results in effective quantum gravity to check the low-energy limit of loop quantum gravity, as well as structure formation in the early universe and possible restrictions on initial states.

Quantum gravity is expected to be important at high energy density, for instance in the early universe during or just after the big-bang. In such regimes, space-time itself, and not just matter in space-time, is described by a wave function subject to quantum uncertainty and fluctuations. For several conceptual and technical reasons, it is difficult to evaluate such wave functions for potential physical observations, but as in particle physics, their implications can often be approximated and derived using effective equations. Standard methods of particle physics are not directly applicable to quantum gravity, in which the classical structure of space-time is no longer available. This project aims to complete the setting of effective equations suitable for quantum gravity, a process in which several questions of mathematical interest (such as Poisson geometry and algebraic structures) will be touched as well. It will contribute to physical cosmology by providing new scenarios and equations for structure formation in the early universe that include quantum-gravity effects.