I am interested in bouncing cosmologies in which the big bang is replaced by a bounce from an earlier, contracting phase to the expanding universe we observe. I want to understand if it is possible to describe such a bounce in the semi-classical limit of quantum gravity, i.e. without having a full fundamental theory that combines the smallest scales (quantum physics) with the highest energies (general relativity).
I work on a new approach to quantize relativistic physics with a path integral over worldlines. An initial wave function over spacetime is propagated and the resulting spacetime amplitude gives the relative probability to find the particle in one spacetime region rather than another. We extend weak values, the outcome of weak measurements first introduced by Aharonov et al, to relativistic worldliness. We can thus describe the quantum particle between two state selections. The framework can be applied to study the Schwinger effect, that is pair creation in an electric field, and also to pair production in de Sitter space.
Moreover, I am interested in the action-at-a-distance formulation by Feynman and Wheeler, based on work by Tetrode and Fokker. Their time-reversal invariant theory describes the motion of elementary particles and their interactions on each other without employing the notion of fields. We would like to extend the Wheeler-Feynman absorber theory of electromagnetism to an action-at-a-distance reformulation of Yang-Mills, and eventually to an action-at-a-distance reformulation of gravity, also building on the work of Hoyle and Narlikar.