Physical Effects of Gravitational Waves at Second Order

TL;DR

This paper addresses the fundamental ambiguity in defining second-order gravitational wave strain in cosmology and demonstrates how to measure its physical effects unambiguously using geodesic observers.

Contribution

It provides the first computation of second-order gravitational wave effects as measured by physical observers, clarifying gauge ambiguities in cosmological perturbation theory.

Findings

Measured strain matches transverse-traceless components in Newton gauge

Clarifies gauge dependence issues at second order

Establishes a physical measurement framework for secondary gravitational waves

Abstract

There is currently no rigorous definition of gravitational wave strain at second order in cosmological perturbation theory. The usual association of gravitational waves with transverse and traceless fluctuations of the metric on spatial hypersurfaces becomes ambiguous at second order, as it inherently depends on the spacetime slicing. While this poses no practical issues in linearized gravity, it presents a fundamental problem for secondary gravitational waves, especially notorious for gravitational waves induced by primordial fluctuations. We compute, for the first time, the physical effects of gravitational waves at second order, as measured by geodesic observers that emit and receive electromagnetic signals, thereby settling the debate on gauge ambiguities. We find that the measured gravitational wave strain coincides with the transverse-traceless components in the Newton gauge.