UBC DG + MP + PDE Seminar: Aidan Chatwin-Davies

A huge challenge for quantum gravity that has impeded the theory's development is how difficult it is to perform experiments. This is mainly because the Planck scale - the energy scale at which both quantum and gravitational effects are inextricably influential - is so far out of reach compared to what we can access in the laboratory. In contrast, the energy scales of the early universe are much closer to the Planck scale. This motivates looking for present-day signatures of Planck-scale physics that trace their origins back to the earliest moments of the universe. The question, then, is what quantum gravitational effects should we look for, and what are their observational signatures is cosmological data that we can measure now? In this talk, I will discuss how a covariant generalization of Nyquist-Shannon sampling theory to Lorentzian manifolds can be used to make a prediction for how a minimal Planckian length scale manifests in the Cosmic Microwave Background, that is, the afterglow of photons that come to us from the Big Bang. Operationally, the apparatus defines a covariant bandlimit, which plays the role of a minimal, diffeomorphism-invariant length scale. Then, discarding contributions to the quantum field theoretic path integral that computes the correlator of cosmic perturbations in the early universe produces a correction to cosmic power spectra that we can access experimentally today. No prior knowledge of cosmology is necessary and we won't actually evaluate any path integrals (we'll just solve some Sturm-Liouville eigenvalue problems instead).