Fast Computation of Bispectrum Features with Generalized Slow Roll

TL;DR

This paper introduces a rapid method based on the generalized slow roll approach for calculating the inflationary curvature bispectrum, achieving high accuracy across all triangle configurations and enabling analysis of models with large bispectra and subtle power spectrum features.

Contribution

The authors develop a fast, accurate technique for computing the inflationary bispectrum using GSR, applicable to models with features and capable of reverse engineering such models.

Findings

Achieves better than 20% accuracy with simple integrals

Improves to better than 5% accuracy with first order GSR

Demonstrates the method on step potential models and confirms bispectrum consistency relations

Abstract

We develop a fast technique based on the generalized slow roll (GSR) approach for computing the curvature bispectrum of inflationary models with features. We show that all triangle configurations can be expressed in terms of three simple integrals over the inflationary background with typical accuracy of better than ~20%. With a first order GSR approach the typical accuracy can be improved to better than the 5% level. We illustrate this technique with the step potential model that has been invoked to explain the WMAP temperature power spectrum glitches at ell ~ 20-40 and show that the maximum likelihood model falls short of observability by more than a factor of 100 in amplitude. We also explicitly demonstrate that the bispectrum consistency relation with the local slope of the power spectrum is satisfied for these models. In the GSR approach, the bispectrum arises from integrals of nearly the same function of the background slow-roll parameters as the power spectrum but with a stronger weight to the epoch before horizon crossing. Hence this technique enables reverse engineering of models with large bispectrum but small power spectrum features.