Bayesian Inferences on Analytical Equations of State Approximations of Neutron Stars
Equations of state (EoS) for dense matter are commonly provided in tabulated pressure-energy density relations, complicating numerical implementation and potentially compromising thermodynamic consistency. In this work, we propose a piecewise-continuous analytical form with a common parametrization capable of representing a broad class of dense matter EoSs. We validate this parametrization against tabulated EoSs from the CompOSE and LALSimulation repositories. Following the initial deterministic fitting, we employed two distinct Bayesian approaches: one based on synthetic EoSs generated by adding noise to the fitted EoS and another based on multi-messenger measurements of neutron-star masses and tidal deformabilities. In both approaches, the initial best-fit parameters are used as reference values. For the considered EoSs, spanning from very soft to very stiff, the resulting fits reproduce the tabulated EoSs and the associated macroscopic neutron-star observables in the repositories with sufficient accuracy. The inferred parameters exhibit strong correlations arising from the continuity conditions imposed at the segment boundaries. These correlations persist in the low- and intermediate-density segments under multi-messenger inference but become weak in the core, reflecting the limited constraining power of current observations at high densities. The ability of a single functional form to describe EoSs derived from different microscopic frameworks, together with the recurrence of similar parameter correlations, suggests that diverse dense matter EoSs may share a common underlying structure.