NSF Award
2308845
A theory of quantum gravity still remains elusive, despite enormous efforts in the past century. Quantum gravity is needed not only for conceptual reasons but also for the understanding of fundamental issues in physics, such as the big bang and black hole singularities. Various candidates have been proposed, and the research supported by this grant is devoted to loop quantum gravity. When applying it to cosmology - the loop quantum cosmology, a coherent picture of Planck scale physics has emerged: the big bang singularity is replaced by a quantum bounce, purely due to quantum geometric effects. This research investigates systematically this and related issues and shall combine studies in challenging physics problems with advanced mathematical methods, which will provide outstanding opportunities for students and collaborators across several different areas of physics and applied mathematics. The theory, techniques and methods to be developed will be used not only in the aforementioned fields, but also in a wider range of fundamental issues in physics and applied mathematics. Particular attention will be put to recruit and attract students from under-represented groups in STEM fields and engineering.<br/><br/>Despite the various successes of Loop Quantum Cosmology (LQC), an important issue is its connection to loop quantum gravity (LQG). The starting point of LQC is first to reduce the Hamiltonian by imposing homogeneity and then to quantize the classically reduced Hamiltonian by using the techniques of LQG. However, in LQG the processes of symmetry reduction and quantization do not commute in general, and it is important to understand how well the physics of the full LQG is captured by LQC. In the past couple of years, modified loop quantum cosmologies have been intensively studied, and the progress made so far is very encouraging, but several fundamental questions still remain, due to the dramatic change of the evolution of the universe in the pre-bounce phase. The research of this award will be devoted to investigating systematically: (i) quantum cosmological perturbations and initial conditions from the full theory of loop quantum gravity; (ii) the evolutions of inhomogeneities, anisotropies and non-Gaussianities; and (iii) resolutions of anomalies found in recent cosmological observations, and observational signals of loop quantum gravity for current and forthcoming observations.<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.
