2025ApJ...988..258V

Sound speed can be an important tool in unravelling the nature of matter at the cores of neutron stars. In this study, we investigate three major classes of equations of state: monotonic, nonmonotonic, and discontinuous, depending on the nature of the sound speed in neutron stars. The monotonic equation of state refers to hadronic models, the nonmonotonic refers to the quarkyonic or smooth crossover models, and discontinuous refers to the first-order phase transition models. We generate a large ensemble of equations of state for three classes with the model-agnostic speed of sound interpolation approach. Further, we find the Bayesian posterior distribution employing the recent astrophysical and gravitational wave constraints. Our main aim is to identify which class of equation of state is most favored by present astrophysical and gravitational wave bounds. The analysis with posterior distribution fails to provide a satisfactory result with the usual neutron star observations like mass-radius and f-mode oscillations. Universal relations are seen as not being really universal, as they show considerable spread and significant overlaps among the different classes. The Bayesian evidence also fails to provide definitive discrimination between the models, though the astrophysical data slightly favors the nonmonotonic equation of state, while the particular gravitational-wave constraints favor the monotonic one.