Infrared Universality of Scalar Induced Gravitational Waves Beyond Second Order
Abstract
Primordial black hole dark matter is formed from the collapse of enhanced primordial density fluctuations. The formation of primordial black holes is accompanied by scalar induced gravitational waves whose infrared scaling only depends on the equation of state, w, of the background at leading order. Establishing whether this characteristic scaling remains robust under corrections of arbitrary perturbative order, including in the presence of non-Gaussianities, requires a physical understanding of the infrared scaling. In this work, we provide such a physical interpretation. We find that the stress of sound waves with nearly equal frequencies produces a slow beat. Although the incoming waves oscillate rapidly, this slow beat continues to source the long wavelength tensor perturbation before its horizon entry, thus generating an infrared scaling that only depends on the expanding background. We show that higher order interactions generate freely propagating waves that finally lead to the same slow beat deep inside the horizon. Since non-Gaussianities would not change the speed of the freely propagating waves, they do not modify the infrared scaling. As the source with a slow beat has enough time to accumulate before the horizon entry of the infrared tensor mode, it records the background expansion and thus the infrared scaling could provide a robust probe of the cosmological equation of state.
Related
- PrimordialPy: A Python library for single-field inflation, primordial black holes, and scalar-induced gravitational waves
- Scalar Perturbations and Induced Gravitational Waves from First-Order Phase Transitions in Lattice Simulations
- Primordial Black Hole Abundances and Scalar Induced Gravitational Waves from Finite-Width Power Spectra in a Stiff Thermal History
- Ultra-slow-roll Inflation with Non-perturbative Non-Gaussianity and Scalar Induced Gravitational Waves
- QCD Crossover Transfer Functions for Scalar-Induced Gravitational Waves in the PTA Band
BibTeX
@misc{yuan2026infrared,
title = {{Infrared Universality of Scalar Induced Gravitational Waves Beyond Second Order}},
author = {Chen Yuan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17928},
eprint = {2609.17928},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17928},
}
RIS
TY - UNPB
TI - Infrared Universality of Scalar Induced Gravitational Waves Beyond Second Order
AU - Chen Yuan
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17928
UR - https://arxiv.org/abs/2609.17928
AB - Primordial black hole dark matter is formed from the collapse of enhanced primordial density fluctuations. The formation of primordial black holes is accompanied by scalar induced gravitational waves whose infrared scaling only depends on the equation of state, w, of the background at leading order. Establishing whether this characteristic scaling remains robust under corrections of arbitrary perturbative order, including in the presence of non-Gaussianities, requires a physical understanding of the infrared scaling. In this work, we provide such a physical interpretation. We find that the stress of sound waves with nearly equal frequencies produces a slow beat. Although the incoming waves oscillate rapidly, this slow beat continues to source the long wavelength tensor perturbation before its horizon entry, thus generating an infrared scaling that only depends on the expanding background. We show that higher order interactions generate freely propagating waves that finally lead to the same slow beat deep inside the horizon. Since non-Gaussianities would not change the speed of the freely propagating waves, they do not modify the infrared scaling. As the source with a slow beat has enough time to accumulate before the horizon entry of the infrared tensor mode, it records the background expansion and thus the infrared scaling could provide a robust probe of the cosmological equation of state.
ER -