NSF Award
2207763
Einstein's General Relativity (GR) is the theory describing the physics of the classical gravitational field. The theory of GR has made tremendous progress in understanding the fundamental aspects of space and time. The theory has been successful in 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 an extremely strong gravitational field, e.g. inside a black hole, or at the very early stage of universe near the big bang. One of the most fundamental open questions in physics is how to complete GR in order to predict physics in an extremely strong gravitational field. The complete theory of gravity that we are searching for is called "Quantum Gravity". The theory of Quantum Gravity should play a crucial role in describing the physics inside a black hole and helping us to understand the early universe near the big bang. Eventually Quantum Gravity will lead us to a revolutionary understanding of space and time, and advance our research of fundamental physics and applications in all aspects. This award supports the development of a candidate Quantum Gravity theory known as "Loop Quantum Gravity" (LQG). This project contains an education plan as part of the broader impact and supports education in physics at both levels of the university and the general public.<br/><br/>LQG is a theory featured with the background independence and non-perturbative quantization of spacetime structure. This project focuses on developing the theory of LQG with cosmological constant in four dimensions, in particular the spinfoam formulation of theory. The main objectives and tasks of this project are: (1) understanding the emergence of smooth curved spacetimes from spinfoams by applying numerical methods to investigate the behavior of spinfoam amplitudes by Pachner moves, (2) developing several aspects of the spinfoam model with cosmological constant, including numerical computations, timelike tetrahedra, the boundary Hilbert space, and geometrical operators, (3) developing the quantum theory of black holes and cosmology with the spinfoam formalism, and investigating numerically the quantum behavior near the singularities from the spinfoam LQG, and (4) clarifying the fermion coupling in LQG, and developing the theory of matter coupling in LQG.<br/><br/>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.
