Loop Quantum Gravity with Cosmological Constant

Einstein's General Relativity is the theory that describes the physics of a classical gravitational field. The theory of General Relativity (GR) is successful in understanding the fundamental aspects of space-time and making predictions for the evolution of the universe and various astrophysical phenomena. However, it is well-known that GR is incomplete. It loses its capability of making predictions in the extremely strong gravitational field (e.g., inside a black hole, or at the very early stage of the Universe during the Big Bang). One of the most fundamental open questions in physics is how to complete GR to predict physics in an extremely strong gravitational field. This project aims toward the complete theory of gravity called "Quantum Gravity". The theory of Quantum Gravity is expected to play a crucial role in describing the physics inside black holes and in the early Universe. Eventually, Quantum Gravity will lead to a revolutionary understanding of space-time and advance the research of fundamental physics as well as applications in all aspects. Additionally, this project includes activities in physics education at university and general public levels. This award supports the development of a candidate Quantum Gravity theory known as "Loop Quantum Gravity" (LQG). LQG is a theory featuring the background independence and non-perturbative quantization of spacetime structure. This project focuses on developing the theory of LQG with cosmological constant in 4 dimensions, in particular, the spinfoam formulation of the theory. The main objectives and tasks of this project are: (1) to advance numerical methods for spinfoam models, both with and without cosmological constant, (2) to develop an effective theory from spinfoam LQG, connecting to the semiclassical consistency, corrections to Einstein gravity, and entanglement entropy, (3) to investigate and understand the physical implications of spinfoam LQG in scenarios such as bouncing cosmology, black-hole-to-white-hole transitions, and matter couplings, and (4) to develop the combinatorial quantization of the SL(2, C) CS theory with a complex level, which underlies the spinfoam model with cosmological constant, and to clarify its relation with the quantum Lorentz group. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.