QCD Crossover Transfer Functions for Scalar-Induced Gravitational Waves in the PTA Band
Abstract
Pulsar timing array (PTA) collaborations have reported evidence for a stochastic gravitational wave (GW) background in the nHz band. Should scalar-induced GWs, sourced at second order by enhanced primordial curvature perturbations, contribute to this signal, a coincidence of scales makes them directly sensitive to the softening of the equation of state around the QCD crossover. We solve the tensor and scalar equations of motion across the Standard Model (SM) thermal history and tabulate the transfer functions for direct use in present and future PTA analyses. We show that this SM effect modifies the height of the induced spectrum by up to ≈55% across the PTA band relative to the radiation-domination expectation, with either sign depending on whether the source modes cross the horizon before or after the crossover. Fitting the NANOGrav 15-year data with a broken-power-law curvature power spectrum, we find that including the crossover shifts the inferred peak amplitude and scale by an amount that could already be relevant for the comparison with primordial black hole overproduction bounds. The importance of this SM effect will grow as the statistical uncertainty on the amplitude and scale shrinks with future, more sensitive PTA datasets, at which point neglecting it could significantly bias the inference.
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
- Infrared Universality of Scalar Induced Gravitational Waves Beyond Second Order
BibTeX
@misc{franciolini2026crossover,
title = {{QCD Crossover Transfer Functions for Scalar-Induced Gravitational Waves in the PTA Band}},
author = {Gabriele Franciolini and Xavier Pritchard and Yuichiro Tada},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29078},
eprint = {2609.29078},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29078},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - QCD Crossover Transfer Functions for Scalar-Induced Gravitational Waves in the PTA Band
AU - Gabriele Franciolini
AU - Xavier Pritchard
AU - Yuichiro Tada
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29078
UR - https://arxiv.org/abs/2609.29078
AB - Pulsar timing array (PTA) collaborations have reported evidence for a stochastic gravitational wave (GW) background in the nHz band. Should scalar-induced GWs, sourced at second order by enhanced primordial curvature perturbations, contribute to this signal, a coincidence of scales makes them directly sensitive to the softening of the equation of state around the QCD crossover. We solve the tensor and scalar equations of motion across the Standard Model (SM) thermal history and tabulate the transfer functions for direct use in present and future PTA analyses. We show that this SM effect modifies the height of the induced spectrum by up to ≈55% across the PTA band relative to the radiation-domination expectation, with either sign depending on whether the source modes cross the horizon before or after the crossover. Fitting the NANOGrav 15-year data with a broken-power-law curvature power spectrum, we find that including the crossover shifts the inferred peak amplitude and scale by an amount that could already be relevant for the comparison with primordial black hole overproduction bounds. The importance of this SM effect will grow as the statistical uncertainty on the amplitude and scale shrinks with future, more sensitive PTA datasets, at which point neglecting it could significantly bias the inference.
ER -