Loop Quantum Gravity and Cosmology: A dynamical introduction

Loop quantum gravity and cosmology are reviewed with an emphasis on evaluating the dynamics, rather than constructing it. The three crucial parts of such an analysis are (i) deriving effective equations, (ii) controlling the theory's microscopic degrees of freedom that lead to its spatial discreteness and refinement, and (iii) ensuring consistency and anomaly-freedom. All three issues are crucial for making the theory testable by conceptual and observational means, and they remain challenging. Throughout this review, the Hamiltonian nature of the theory will play a large role for properties of space-time structure within the framework discussed.