Quantum Field Theory and Cosmology

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During the earliest moments of its existence the Universe underwent such rapid, and accelerated, expansion that quantum fluctuations were ripped out of empty space to produce a vast, and ever-growing ensemble of gravitational radiation. This radiation provided a sort of medium which affected long range forces and also how things propagate, the same way that water changes electric forces and the propagation of light. Because ever-more radiation was produced, its effects grew with time, and sometimes also with space. It is possible that remnants of these effects became strong enough to survive to the current day, and that they provide explanations for some of the puzzles which arise when one tries to understand the large scale Universe in terms of ordinary matter with Einstein’s theory of gravitation. The goal of this project is to develop reliable techniques for calculating these effects when they become strong, and modeling the results as changes in Einstein’s theory of gravitation. The project involves extensive international collaborations with physicists in the Czech Republic, France, Greece, Netherlands and Taiwan. The project provides summer support for two graduate students per year, whose education enhances the pool of STEM talent available to the United States. It should also be noted that, although the PI selects students on the basis of merit, over half of his past graduate students have been female or Hispanic. During the fall of 2021 the PI and collaborators showed that the large logarithms induced by nonlinear sigma models (whose derivative interactions mimic those of gravity) on de Sitter background can be summed up by combining variants of Starobinsky's stochastic formalism and the renormalization group. They also demonstrated that that the exchange potential of a massless, minimally coupled scalar (MMCS) provides the simplest venue for purging gauge dependence by including quantum gravitational correlations from the source and observer. The recent breakthrough on resummation, coupled with steady progress on approximating effective potentials in realistic geometries, has also provided important insights for expressing graviton loop corrections in terms of simple, nonlocal modifications of gravity. Finally, the effective potential results suggest a dramatic simplification for computations of reheating from longitudinal vectors. To exploit this recent progress the PI and his graduate students will continue their collaborations with Dr. Drazen Glavan (CEICO, Czech Republic), Prof. Cedric Deffayet (IAP, France), Prof. Shun-Pei Miao (NCKU, Taiwan), Prof. Tomislav Prokopec (U. Utrecht, Netherlands) and Prof. Nikolaos Tsamis (U. Crete, Greece) on four main projects: Generalize the new resummation technique to quantum gravity; demonstrate that source and observer correlations eliminate gauge dependence in the MMCS exchange potential on de Sitter background; develop and explore nonlocal modifications of gravity; and show how reheating can be analyzed using cosmological Coleman-Weinberg potentials.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.