On the Gauge Invariance of Secondary Gravitational Waves

TL;DR

This paper introduces a boundary condition-based filtering method that ensures gauge invariance of the energy density of secondary gravitational waves, improving the physical consistency of cosmological perturbation analyses.

Contribution

The authors develop a novel filtering technique based on the Sommerfeld criterion to extract physical gravitational wave modes, addressing gauge dependence issues in second-order perturbation theory.

Findings

Gauge-invariant energy density after filtering

Consistent behavior in the sub-horizon limit

Unified treatment for adiabatic and isocurvature perturbations

Abstract

Second-order tensor perturbations induced by primordial fluctuations play a crucial role in probing small-scale physics, but gauge dependence of their energy density has remained a fundamental challenge in cosmological perturbation theory. We address this issue by introducing a boundary condition-based filtering method that extracts physical radiation through the Sommerfeld criterion. We demonstrate that after filtering non-physical modes, the energy density of secondary gravitational waves becomes gauge-invariant and exhibits physically consistent behavior in the sub-horizon limit. This approach provides a unified framework for both adiabatic and isocurvature perturbations, enhancing theoretical predictions and observational signatures of early universe physics.