Bispectrum in Single-Field Inflation Beyond Slow-Roll

TL;DR

This paper introduces a new integral form for the bispectrum in single-field inflation models that relaxes slow-roll constraints, enabling efficient analysis of models with rapid background evolution and providing tools to distinguish between different inflation scenarios.

Contribution

It develops a general integral form for the bispectrum applicable beyond slow-roll, including analytic solutions for models with sharp features, and preserves key consistency relations.

Findings

The integral form allows fast evaluation of the bispectrum across all configurations.

Analytic solutions for bispectrum peaks in models with sharp steps in warp tension.

The bispectrum can distinguish models with similar power spectra but different underlying physics.

Abstract

We develop an integral form for the bispectrum in general single-field inflation whose domain of validity includes models of inflation where the background evolution is not constrained to be slowly varying everywhere. Our integral form preserves the squeezed-limit consistency relation, allows for fast evaluation of the bispectrum for all triangle configurations expediting the efficient comparison of slow-roll violating models with data, and provides complete and compact slow-roll expressions correct to first order in slow-roll parameters. Motivated by the recent Planck results, we consider as an example a sharp step in the warped-brane tension of DBI inflation and provide analytic solutions for the peak of the resulting bispectrum. For the step in the warp that reproduces the oscillations in the power spectrum favored by the Planck data, the corresponding equilateral bispectrum is both extremely large and highly scale dependent. The bispectrum serves as a means of distinguishing such a model from alternative scenarios that generate otherwise indistinguishable power spectra, such as a step in the potential in canonical single-field inflation.