The general behavior of the nuclear equation of state (EOS), relevant for the description of neutron stars (NSs), is studied within a Bayesian approach applied to a set of models based on a density-dependent relativistic mean-field description of nuclear matter. The EOS is subjected to a minimal number of constraints based on nuclear saturation properties and the low-density pure neutron matter EOS obtained from a precise next-to-next-to-next-to-leading order (N³LO) calculation in chiral effective field theory (χEFT). The posterior distributions of the model parameters obtained under these minimal constraints are employed to construct the distributions of various nuclear matter properties and NS properties such as radii, tidal deformabilities, central energy densities, speeds of sound, etc. We found that a 90% confidence interval for the allowed NS mass–radius relationship and tidal deformabilities is compatible with GW170817 and recent Neutron star Interior Composition ExploreR observations, without invoking the exotic degrees of freedom. A central speed of sound of the order of 2 / 3 c is obtained. The maximum NS mass allowed by the model is 2.5 M _⊙.

The high-density behavior of nuclear matter is analyzed within a relativistic mean field description with nonlinear meson interactions. To assess the model parameters and their output, a Bayesian inference technique is used. The Bayesian setup is limited only by a few nuclear saturation properties, the neutron star maximum mass larger than $2M_{\odot }$, and the low-density pure neutron matter equation of state (EOS) produced by an accurate ${\mathrm{N}}^3\mathrm{LO}$ calculation in chiral effective field theory. Depending on the strength of the nonlinear scalar vector field contribution, we have found three distinct classes of EOSs, each one correlated to different star properties distributions. If the nonlinear vector field contribution is absent, the gravitational maximum mass and the sound velocity at high densities are the greatest. However, it also gives the smallest speed of sound at densities below three times saturation density. On the other hand, models with the strongest nonlinear vector field contribution predict the largest radii and tidal deformabilities for $1.4M_{\odot }$ stars, together with the smallest mass for the onset of the nucleonic direct Urca processes and the smallest central baryonic densities for the maximum mass configuration. These models have the largest speed of sound below three times saturation density, but the smallest at high densities, in particular, above four times saturation density the speed of sound decreases approaching approximately $\sqrt{0.4}c$ at the center of the maximum mass star. On the contrary, a weak nonlinear vector contribution gives a monotonically increasing speed of sound. A $2.75M_{\odot }$ neutron star (NS) maximum mass was obtained in the tail of the posterior with a weak nonlinear vector field interaction. This indicates that the secondary object in GW190814 could also be an NS. The possible onset of hyperons and the compatibility of the different sets of models with perturbative QCD (pQCD) are discussed. It is shown that pQCD favors models with a large contribution from the nonlinear vector field term or which include hyperons.

We explore supervised machine learning methods in extracting the non-linear maps between neutron stars (NS) observables and the equation of state (EoS) of nuclear matter. Using a Taylor expansion around saturation density, we have generated a set of model independent EoS describing stellar matter constrained by nuclear matter parameters that are thermodynamically consistent, causal, and consistent with astrophysical observations. From this set, the full non-linear dependencies of the NS tidal deformability and radius on the nuclear matter parameters were learned using two distinct machine learning methods. Due to the high accuracy of the learned non-linear maps, we were able to analyze the impact of each nuclear matter parameter on the NS observables, identify dependencies on the EoS properties beyond linear correlations and predict which stars allow us to draw strong constraints.

We describe charge-neutral neutron star matter in $\beta$-equilibrium using hybrid equations of state (EOSs), where a first-order phase transition from hadronic to quark matter is realized. The hadronic matter is described in a model-independent way by a Taylor expansion around saturation density $n_0$, while the three-flavor Nambu–Jona-Lasinio (NJL) model is used for the quark matter. Exploring the present uncertainty on the empirical parameters of nuclear matter and the parameter space of the NJL model, we construct two data sets of thermodynamically consistent and causal hybrid EOSs, compatible with astrophysical observations. We conclude that, to sustain a considerable quark core size, the intensity of the phase transition from hadron to quark matter cannot be strong, having an energy density gap below $200\mathrm{MeV}/{\mathrm{fm}}^3$, and must occur at baryon densities not above 4 times the saturation density. A nonzero but not too strong quark vector-isoscalar term and a weak vector isovector quark term are required. Large quark cores carrying almost half of the star mass are possible inside neutron stars with a maximum mass $\approx 2.2M_{\odot }$. To get a considerable number of hybrid EOSs predicting quark matter already inside neutron stars with a mass $\sim 1.4M_{\odot }$, we require that the onset of quarks occurs in the range $1.3n_0$ and $2.5n_0$. Neutron stars with large quark cores corresponding to more than one fourth of the total star mass are possible if the energy density gap and the pressure at transition are below $100\mathrm{MeV}/{\mathrm{fm}}^3$. However, under these constraints, the maximum neutron star mass is limited to $\lesssim 2.06M_{\odot }$. No strong signatures from quark matter were found on the radius and the tidal deformability for neutron star masses below $1.8M_{\odot }$.

The effect of a strong magnetic field on the location of the critical end point (CEP) in the QCD phase diagram is discussed under different scenarios. In particular, we consider the contribution of the vector interaction and take into account the inverse magnetic catalysis obtained in lattice QCD calculations at zero chemical potential. The discussion is realized within the ($2+1$) Polyakov–Nambu–Jona-Lasinio model. It is shown that the vector interaction and the magnetic field have opposite competing effects, and that the winning effect depends strongly on the intensity of the magnetic field. The inverse magnetic catalysis at zero chemical potential has two distinct effects for magnetic fields above $\gtrsim 0.3{\mathrm{GeV}}^2$: it shifts the CEP to lower chemical potentials, hinders the increase of the CEP temperature and prevents a too large increase of the baryonic density at the CEP. For fields $eB<0.1{\mathrm{GeV}}^2$ the competing effects between the vector contribution and the magnetic field can move the CEP to regions of temperature and density in the phase diagram that could be more easily accessible to experiments.

The location of the critical end point (CEP) in the QCD phase diagram is determined under different scenarios. The effect of strangeness, isospin/charge asymmetry and an external magnetic field is investigated. The discussion is performed within the $2+1$ flavor Nambu\char21{}Jona-Lasinio model with Polyakov loop. It is shown that isospin asymmetry shifts the CEP to larger baryonic chemical potentials and smaller temperatures. At large asymmetries the CEP disappears. However, a strong enough magnetic field drives the system into a first order phase transition.