Grants and Contributions:

Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023)

The physics of the small, at the scale of atomic and nuclear phenomena, is described by quantum theory. We now have broadly successful quantum theories that describe three of the four observed fundamental forces in nature: electromagnetic, weak and strong nuclear interactions. On the other hand, physics on large scales, encompassing the study of solar systems, galaxies and cosmology as a whole, is described by a gravitational theory, the most successful of which is Einstein's theory of general relativity. This theory envisions gravity as a curvature of the geometry of space and time, welded together as one entity: spacetime.
Quantum theory is expected to be important in gravitational phenomena involving very strong gravitational fields of highly compact objects, such as black holes and the very early Universe. Combining gravitation with quantum theory is widely considered to be the frontier problem in theoretical physics, and would reveal a "quantum geometry" with matter.
The purpose of the proposed research is to explore one approach to developing a quantum theory of gravity. This requires the use of a clock as a part of the description of geometry and matter, and helps us to clarify what is meant by "energy of the Universe." I will use this description, called the Hamiltonian theory, to study the properties of the early Universe very close to the Big Bang, and the formation of black holes, using computer simulations.
These simulations will use a method of random sampling of the state of gravity and matter known as the Monte Carlo method. This is a very efficient and well-developed technology that has wide ranging applications, but it has so far not been applied to the study of matter and the geometry of the Universe in a fully quantum setting. This method is expected to reveal properties called phase transitions, that are familiar in solid, liquid and gas phases of matter. But if the physical system is gravity and matter, with gravity described as a spacetime curved geometry, the phases could turn out to be unusual and revealing. One interesting feature is the correlation length. This is a measure of how far apart in space physical effects are correlated. If this distance is very large, it means that very distant physical phenomena are related, or march in step. An infinite correlation length signals a phase transition.
I expect the ideas and methods to be employed in this proposal will provide new insights into the problem of quantum gravity. These insights could guide future theoretical developments, and provide a better understanding of cosmological problems, such as dark matter and energy. The simulation methods to be used have diverse applicability, from forecasting polls to analyzing big data sets, and therefore provide important multi-disciplinary tools for training HQP.