PHYSICS DISSERTATION DEFENSE: Dayshon Mathis
Ph.D. Candidate: Dayshon Mathis
Research Advisor: Eva Silverstein
Date: May 31, 2023
Time: 2 pm
Location: PAB 102/103
Zoom Link: https://stanford.zoom.us/j/3092253373
Zoom Password: email nickswan [at] stanford.edu (nickswan[at]stanford[dot]edu) for password.
Title: Novel Inflation and Black Hole Dynamics with Application
Abstract: Black holes are interesting astrophysical objects that have been studied as systems sensitive to quantum gravitational data. The accelerated geometry in the exterior of extremal black holes can induce large center-of-mass energies between particles with particular momenta at the horizon. This is known as the Bañados-Silk-West (BSW) effect. For point particles, the BSW effect requires tuning to have the collision coincide with the horizon. However, this tuning is relaxed for string-theoretic objects. String scattering amplitudes are large in the Regge limit which occurs at large center-of-mass energies and shallow scattering angles, parametrically surpassing quantum field theoretic amplitudes. In this limit, longitudinal string spreading is induced between strings with a large difference in light-cone momenta, and this spread can be used to ‘detune’ the BSW effect. With this in mind, quantum gravitational data, as described by string theory, may play an important role in near horizon dynamics of extremal Kerr black holes. Further, though it may be hard to realize astrophysically, this system acts as a natural particle accelerator for probing the nature of small-scale physics at Planckian energies.
The inflationary epoch of the early universe described by the rapid acceleration of space, was introduced to explain the distribution of matter in our universe. In particular, models using ‘slow-roll inflation’ have been successful in predicting this distribution, as have more general models with stronger interactions, such as DBI inflation obtained from a gauge theory with many ‘color’ degrees of freedom. We find a novel analogous mechanism for inflation by coupling the scalar field governing the expansion, the inflaton, to a family of flavor fields. Its effective action leads to a Coleman-Wienberg potential term that generates viable inflation, via a speed limit deriving from a logarithmic-- rather than a square root-- branch cut. Interestingly, a version of the model can be cast as an energy-conserving-descent optimization algorithm. A machine learning algorithm utilizing this logarithmic Hamiltonian has interesting properties for finding minimal loss solutions while effectively spanning large regions of phase space.