MC 5158
Candidate
Aidan Chatwin-Davies, Applied Mathematics, University of Waterloo
Title
A Covariant Natural Ultraviolet Cutoff in Inflationary Cosmology
Abstract
In the field of quantum gravity, it is widely expected that some form of a minimum length scale, or ultraviolet cutoff, exists in nature. So far, most studies of ultraviolet cutoffs have been concerned with Lorentz-violating cutoffs. Recently, however, a natural ultraviolet cutoff that is fully covariant was proposed. With this cutoff, field modes with arbitrarily small wavelengths still exist, albeit with exceedingly small, covariantly-determined bandwidths.
The effects of this covariant ultraviolet cutoff on the dynamics of a scalar quantum field are of great interest for cosmology. This is because their presence may have direct observational signatures in the statistic of the cosmic microwave background. As such, this covariant ultraviolet cutoff offers the tantalizing prospect of experimental access to physics the Planck scale.
This work culminates in an explicit calculation of the effect of this covariant cutoff on the dynamics of a scalar quantum field in power-law Friedman-Lemaitre-Robertson-Walker (FLRW) spacetime. Such a spacetime is a prototypical and realistic model for early-universe inflation. In preparation for studying the covariant cutoff on curved spacetime, I will review the necessary background material as well as the kinematic influence of the covariant cutoff. I will also discuss several side results that I have obtained on scalar quantum field theories in spacetimes which possess a finite start time.