The Cosmological Bootstrap

This project will aim to develop new mathematical techniques that will enable us to more efficiently compute cosmological correlators, which are the fundamental observables in early universe cosmology, and provide us with a better understanding of their fundamental structures.

The project will aim to derive a classification of primordial non-Gaussianities which are one of the primary detection goals of the large number of current and upcoming Cosmic Microwave Background and Large-Scale Structure surveys. Such a classification, which will be based on symmetries and field content, will enable us to straightforwardly learn about theories of early universe cosmology given a detection of non-Gaussianities. The classification will focus on all three-point functions between gravitons and curvature perturbations. These three-point functions will be bootstrapped using a combination of symmetries, locality and unitarity and by demanding that together they form consistent four-point functions.

The project will also aim to derive recursion relations from which higher-point cosmological correlation functions can be computed from lower points ones. The focus will be on both scalar effective field theories, and theories of massless spinning fields such as Yang-Mills and gravity. For scalar effective field theories with non-linearly realised symmetries we expect such recursion relations to exist, while for theories of massless spinning fields gauge invariance suggests the existence of such relations. Guidance will come from recursion relations for scattering amplitudes in flat-space, given that these amplitudes are contained within their cosmological counterparts.

The student leading these projects will be working within one of the most exciting and fastest growing areas of theoretical cosmology. The student will also benefit from a very lively UK and international community of researchers working in this field which now sits at the forefront of theoretical cosmology.