Bayesian inference of the dense matter equation of state built upon extended Skyrme interactions

The non-relativistic model of nuclear matter with Brussels extended Skyrme interactions is employed in order to build, within a Bayesian approach, models for the dense matter equation of state (EOS). In addition to a minimal set of constraints on nuclear empirical parameters; the density behavior of the energy per particle in pure neutron matter (PNM); a lower limit on the maximum neutron star (NS) mass, we require that the Fermi velocity of neutrons ($v_{\mathrm{F;\,n}}$) in PNM and symmetric nuclear matter (SNM) with densities up to $0.8~\mathrm{fm}^{-3}$ (arbitrary) does not exceed the speed of light. The latter condition is imposed in order to cure a deficiency present in many Skyrme interactions [Duan and Urban, Phys. Rev. C 108, 025813 (2023)]. We illustrate the importance of this constraint for the posterior distributions. Some of our models are subjected to constraints on the density dependence of neutron (nucleon) Landau effective mass in PNM (SNM), too. The impact of various sets of constraints on the behaviors of nuclear matter and NSs is discussed in detail. Systematic comparison with results previously obtained by employing Skyrme interactions is done for posteriors of both nuclear matter (NM) and NS parameters. Special attention is given to the model and constraints dependence of correlations among various quantities.