\delta N Formalism in Anisotropic Inflation and Large Anisotropic Bispectrum and Trispectrum

TL;DR

This paper develops a elta N formalism for anisotropic inflation, enabling calculation of power spectrum, bispectrum, and trispectrum, revealing large anisotropic non-Gaussianities consistent with observations.

Contribution

It introduces a elta N formalism tailored for anisotropic backgrounds, matching in-in formalism results and analyzing anisotropic non-Gaussianities in inflation.

Findings

Power spectrum anisotropies are kept small to satisfy observational constraints.

Large orientation-dependent non-Gaussianities can be generated.

The Suyama-Yamaguchi inequality is studied in anisotropic contexts.

Abstract

We present a consistent \delta N formalism for curvature perturbations in anisotropic cosmological backgrounds. We employ our \delta N formalism to calculate the power spectrum, the bispectrum and the trispectrum in models of anisotropic inflation with the background gauge fields in Bianchi I universe. Our results coincide exactly with the recent results obtained from in-in formalism. To satisfy the observational constraints the anisotropies generated on power spectrum are kept small but large orientation-dependent non-Gaussianities can be generated. We study the Suyama-Yamaguchi inequality for the amplitudes of the bispectrum and the trispectrum in the presence of anisotropic shapes.