Statistical anisotropy of primordial gravitational waves from generalized $\delta N$ formalism

TL;DR

This paper introduces a generalized $ abla$ formalism to analytically connect primordial gravitational wave fluctuations at horizon crossing with their evolution, including anisotropic inflation models, revealing conditions for polarization.

Contribution

It develops an analytic formula using the Noether charge density within the generalized $ abla$ formalism to relate horizon crossing fluctuations to gravitational waves, applicable to anisotropic inflation.

Findings

Derived an analytic mapping formula for gravitational waves.

Identified conditions for non-zero linear polarization.

Compared single- and multi-gauge field inflation models.

Abstract

In this letter, we demonstrate how to use the generalized $\delta N$ formalism, which enables us to compute the evolution of all the large scale fluctuations, including gravitational waves, solely by solving the evolution of the background homogeneous Universe. Using the Noether charge density, we derive an analytic formula which describes the mapping between the fluctuations at the horizon crossing and the sourced gravitational waves at the end of inflation. This formula can apply also to an inflation model with an anisotropic background. Using this formula, we discuss the condition for the non-vanishing linear polarization and the qualitative difference between single- and multi-gauge field models.