g$\delta N$ formalism

TL;DR

This paper extends the $ abla N$ formalism to a generalized version capable of computing scalar, vector, and tensor perturbations, including gravitational waves, with applications demonstrated in a U(1) gauge field model.

Contribution

It introduces the g$ abla N$ formalism, a comprehensive framework for analyzing various perturbations, and discusses its application to gauge fields and gravitational wave polarization differences.

Findings

The formalism allows calculation of different polarization amplitudes of GWs.

Application to a U(1) gauge field model demonstrates the formalism's utility.

Discussion of Weinberg's adiabatic mode in anisotropic backgrounds.

Abstract

The $\delta N$ formalism has been the major computational tool to study the superhorizon evolution of the scalar type perturbation sourced by scalar fields. Recently, this formalism was generalized to compute an arbitrary scalar, vector, and tensor type perturbations, including the gravitational waves (GWs), sourced by an arbitrary bosonic fields. In this paper, we explain how to use the generalized $\delta N$ formalism (the g$\delta N$ formalism), considering a model with U(1) gauge fields as a concrete example. Several new findings on this model and prospects on future gravitational wave experiments are also discussed, including the condition for the two linear polarizations of GWs to have different amplitudes. This paper provides a detailed explanation of our previous paper published in Physical Review Letters. We also discuss the Weinberg's adiabatic mode for an anisotropic background, showing a qualitative difference from the one for the FLRW background.