Multi-field inflation with non-minimally coupled fields: theoretical predictions and observational constraints

In the two-field inflationary paradigm, it is commonly assumed that the kinetic coupling between the fields, resulting from a non-minimal coupling in the Jordan frame and leading to a curved field manifold in the Einstein frame, depends solely on one field. Our study delves into the situation where the kinetic coupling can instead vary with both fields. The aim of this study is to investigate adiabatic and isocurvature perturbations within these extended theories. Our analysis reveals that, while the evolution equation for the curvature perturbation remains unchanged when allowing coupling dependence on both fields, the effective mass of the entropy perturbation undergoes modifications. We analytically study the correlations between the models’ free parameters and present also a novel numerical method tailored to the study of general multi-field models. Our algorithm captures the dynamics of the fields throughout the entire inflationary phase, providing accurate predictions for observables such as the spectrum of primordial scalar perturbations, primordial gravitational waves, isocurvature modes, and the transfer of entropy to scalar modes after the horizon crossing. By sampling over the initial conditions of the fields and the free parameters of the model, we enable a Monte Carlo analysis, testing the theoretical predictions against observational data.