Bayesian evidence for two peaks in the sound speed in cold dense QCD

I show that in addition to the well-known peak inside massive neutron stars, the sound speed in cold dense QCD matter likely exhibits another peak above neutron star densities before it asymptotes to $c_s=\sqrt{C_s}=\sqrt{1/3}$. Based on the framework reported in arxiv:2408.16738, this approach does not rely on any assumption about the ultra-dense matter not realized in nature. Current multimessenger observation of neutron stars favors the two-peak scenario with a Bayes factor $5.1_{-0.7}^{+0.9}$, where the uncertainties are systematics due to models of neutron star inner cores. This evidence grows to $27_{-8}^{+11}$ if the $2.6M_\odot$ component of GW190814 is a neutron star. The trough in $C_s$ separating the two peaks is inferred to be below $0.05^{+0.04}_{-0.02}$ (at the $50\%$ level) if $2.6M_\odot$ neutron stars exist. The second peak above $1/3$ beyond baryon chemical potential $\mu_B=1.6-1.9$ GeV most likely signals non-perturbative effects in cold quark matter, for instance color superconductivity.