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 for understanding the very origin of our universe, the big bang. Remarkable progress in understanding the big bang has occurred through the use of loop quantum cosmology (LQC), a simplified version of loop quantum gravity (LQG) for modeling the universe as a whole. This award seeks to bridge the gap between LQC and full LQG. Such a bridge would allow future comparisons of LQC with data to tell us exact details about the fundamental laws of quantum gravity. Bridging this gap requires answering a number of interesting fundamental conceptual questions. 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 publication and scientific lectures, as well as to the general public through public lectures and other means.
With this award, the observational, cosmological consequences of different proposals for dynamics in LQG will be studied. To accomplish this, the PI will first find an embedding of LQC states into diffeomorphism invariant LQG states that satisfy the diffeomorphism invariant, quantum criterion for homogeneity and isotropy recently established by the PI's group. This embedding, appropriately regularized, will enable different proposals for dynamics in LQG to be translated into LQC, and thereby to distinguish their observational consequences using established methods. The task of finding the corresponding LQC dynamics will be simplified by the fact that the resulting possibilities are severely restricted by diffeomorphism invariance, as proven recently by the PI's group. The PI also 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 what is called the proper spin-foam model. Since then, other research groups have indicated how this modified model may solve a number of long-standing issues in spin-foams. These possibilities, as well as other issues in spin-foams, will be investigated with the present award.
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.
