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In this paper, we analyse sound waves arising from a cosmic phase transitionwhere the full velocity profile is taken into account as an explanation for thegravitational wave spectrum observed by multiple pulsar timing array groups.Unlike the broken power law used in the literature, in this scenario the powerlaw after the peak depends on the macroscopic properties of the phasetransition, allowing for a better fit with pulsar timing array (PTA) data. Wecompare the best fit with that obtained using the usual broken power law and,unsurprisingly, find a better fit with the gravitational wave (GW) spectrumthat utilizes the full velocity profile. We then discuss models that canproduce the best-fit point and complementary probes using CMB experiments andsearches for light particles in DUNE, IceCUBE-Gen2, neutrinoless double betadecay, and forward physics facilities at the LHC like FASER nu, etc.

Did we hear the sound of the Universe boiling? Analysis using the full fluid velocity profiles and NANOGrav 15-year data