Reconciling quantum fields with gravity in the universe

We plan to investigate foundational questions regarding the role of quantum fields in cosmology. As is well known, the gauge and fermion fields in the standard model of particle physics contribute divergent "zero-point" vacuum energy. Furthermore, in a curved background spacetime the local scale symmetry of the classical theory is broken by quantum stress-energy "trace anomalies." A possible resolution of these puzzles involves including four-derivative dimension zero scalar fields. These fields may also explain the large scale density density perturbations observed in cosmology. Their quantization is subtle due to potential ghosts and classical instabilities. In the free theory and conformally flat spacetime, these are removed with a physical state constraint, leaving the vacuum as the only physical state. Our initial project will be to investigate interacting dimension zero fields and their effect when coupled to gravity, quantum mechanically.