Numerical evaluation of inflationary 3-point functions on curved field space

TL;DR

This paper extends a computational tool to evaluate the three-point correlation functions in multi-field inflation models with curved field space, including effects like particle production, and applies it to analyze non-Gaussian signals.

Contribution

The authors enhance the CppTransport code to handle curved field space in multi-field inflation, enabling detailed analysis of non-Gaussianities with improved numerical validation.

Findings

Excellent agreement between Cartesian and polar coordinates implementations.

Good consistency with PyTransport 2.0 results.

Enhanced non-Gaussian signals are hard to produce with simple hyperbolic geometries.

Abstract

We extend the public CppTransport code to calculate the statistical properties of fluctuations in multiple-field inflationary models with curved field space. Our implementation accounts for all physical effects at tree-level in the 'in-in' diagrammatic expansion. This includes particle production due to time-varying masses, but excludes scenarios where the curvature perturbation is generated by averaging over the decay of more than one particle. We test our implementation by comparing results in Cartesian and polar field-space coordinates, showing excellent numerical agreement and only minor degradation in compute time. We compare our results with the PyTransport 2.0 code, which uses the same computational approach but a different numerical implementation, finding good agreement. Finally, we use our tools to study a class of gelaton-like models which could produce an enhanced non-Gaussian signal on equilateral configurations of the Fourier bispectrum. We show this is difficult to achieve using hyperbolic field-space manifolds and simple inflationary potentials.