Multifield inflation and differential geometry

Abstract

Cosmic inflation posits that the universe underwent a period of exponential expansion, driven by one or several quantum fields, shortly after the Big Bang. Renormalization requires the fields be non-minimally coupled to gravity. We examine such multifield models and find a rich geometric structure. After a conformal transformation of spacetime, the target field-space acquires non-trivial curvature. We explore two main consequences. First, we construct a field-space covariant framework to study quantum perturbations, extending prior work beyond the slow-roll approximation by working on the full phase space of the theory. Secondly, we show that a wide class of inflationary models can be understood as a geodesic motion on a suitably related manifold. Our geometric approach provides great insight into the (classical) field dynamics, and we have used them to compute non-gaussianities in the cosmic microwave background radiation spectrum.