NSF Award
2409018
An important question facing fundamental physics is how the well-tested laws of Einstein's theory of gravity and quantum mechanics are consistent - the question of quantum gravity. This question is central to understanding the very origin of our universe, the Big Bang, as well as for understanding the final fate of black holes. The award seeks to bridge the gap between the full theory of loop quantum gravity (LQG) and simplified models of cosmology and black holes based on LQG that have been recently successful in making potential observational predictions. Such a bridge would allow future comparisons of such models with data to tell us exact details about the fundamental laws of quantum gravity. A second part of this research aims to answer key questions regarding the Feynman sum-over-histories formulation of loop quantum gravity, in which space and time are treated in a more unified way, and to bring this formulation closer to completion. By enabling graduate students to participate in frontier physics, and to interact with other research groups, this award will have a broad and long-term impact on the development of future scientists. The results of the research will be disseminated to the scientific community through peer-reviewed publications and scientific lectures, as well as to the general public through public lectures. <br/> <br/>The observational consequences, for both cosmology and black holes, of different possible dynamics in LQG will be determined. To accomplish this, the PI will first find an embedding of states from the appropriate simplified quantum model - Loop Quantum Cosmology (LQC) or Loop Quantum Kantowski-Sachs (LQKS) - into diffeomorphism-invariant LQG states that satisfy the quantum criterion for homogeneity and isotropy recently established by the PI’s group. This embedding will enable different possible dynamics in LQG to be translated into LQC and LQKS, and thereby to distinguish their observational consequences using established methods. The task of finding the corresponding LQC/LQKS dynamics is simplified by the severe restriction on the resulting possibilities proven, over the last 6 years by the PI’s group, from diffeomorphism invariance. The PI additionally plans to further develop the sum over histories approach to LQG, known as spin-foams. In prior work of the PI, the prevailing EPRL model of spin-foams was modified to correct its semiclassical limit, yielding the `proper spin-foam model’. Efficient numerical methods will be developed to perform calculations using this model. Possibilities for solving long-standing issues in spin foams, as well as applications to the thermodynamics of the quantum gravitational field, will be explored.<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.
