Primordial Power Spectrum and Bispectrum from Lattice Simulations of Axion-U(1) Inflation

TL;DR

This paper introduces a high-precision lattice simulation code for axion-U(1) inflation, predicting primordial non-Gaussianity and providing new methods to constrain inflationary parameters from the bispectrum.

Contribution

The paper presents a novel high-precision lattice simulation approach for axion-U(1) inflation, including detailed predictions of the power spectrum and bispectrum with new fitting functions.

Findings

Power spectrum and bispectrum exhibit a strong blue tilt.

Fitting functions accurately reproduce simulation statistics.

Results show non-separable bispectrum shapes, challenging standard non-Gaussianity models.

Abstract

We present primordial non-Gaussianity predictions from a new high-precision code for simulating axion-U(1) inflation on a discrete lattice. We measure the primordial scalar curvature power spectrum and bispectrum from our simulations, determining their dependence on both scale and axion-gauge coupling strength. Both the gauge-sourced power spectrum and the bispectrum exhibit a strong blue tilt due to our choice of an $\alpha$-attractor inflaton potential. We provide fitting functions for the power spectrum and bispectrum that accurately reproduce these statistics across a wide range of scales and coupling strengths. While our fitting function for the bispectrum has a separable form, results from high-resolution simulations demonstrate that the full shape is not separable. Thus, our simulations generate realizations of primordial curvature perturbations with nontrivial correlators that cannot be generated using standard techniques for primordial non-Gaussianity. We derive bounds on the axion-gauge coupling strength based on the bispectrum constraints from the cosmic microwave background, demonstrating a new method for constraining inflationary primordial non-Gaussianity by simulating the nonlinear dynamics.