On the Gauge Invariance of Secondary Gravitational Waves
arXiv:2501.13691 · doi:10.1088/1475-7516/2025/07/016
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.
arXiv commentv3, 15 pages, 2 figures, JCAP accepted
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