Footprints of the QCD Crossover on Cosmological Gravitational Waves at Pulsar Timing Arrays

Pulsar timing arrays (PTAs) have reported evidence for a stochastic gravitational wave (GW) background at nanohertz frequencies, possibly originating in the early Universe. We show that the spectral shape of the low-frequency (causality) tail of GW signals sourced at temperatures around <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>T</a:mi><a:mo>≳</a:mo><a:mn>1</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>GeV</a:mi></a:mrow></a:math> is distinctively affected by confinement of strong interactions (QCD), due to the corresponding sharp decrease in the number of relativistic species, and significantly deviates from <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mo>∼</c:mo><c:msup><c:mi>f</c:mi><c:mn>3</c:mn></c:msup></c:math> commonly adopted in the literature. Bayesian analyses in the NANOGrav 15 years and the previous international PTA datasets reveal a significant improvement in the fit with respect to cubic power-law spectra, previously employed for the causality tail. While no conclusion on the nature of the signal can be drawn at the moment, our results show that the inclusion of standard model effects on cosmological GWs can have a decisive impact on model selection.