The possibility of modifications on general relativity is investigated. We propose an alternative theory of gravity constructed with the combination of Rastall and rainbow theories. The hydrostatic equilibrium equations are obtained in order to test the new theory in neutron stars, whose mass-radius diagrams are obtained using modern equations of state of nuclear matter derived from relativistic mean field models and compared with the ones computed by the Tolman-Oppenheimer-Volkoff equations. Different sets of parameters are used and the obtained results confronted with accepted masses and radii values, including important astrophysical objects as the quiescent LMXB NGC 6397 and the double neutron system J0737. We conclude that substantial modifications are obtained even for very small alterations on the two free parameters, making the reproduction of astrophysical observations an easier task.

A compressible liquid-drop model (CLDM) is used to correlate uncertainties associated with the properties of the neutron star (NS) crust with theoretical estimates of the uncertainties associated with the equation of state (EOS) of homogeneous neutron and nuclear matter. For the latter, we employ recent calculations based on Hamiltonians constructed using chiral effective-field theory ($\chi \mathrm{EFT}$). Fits to experimental nuclear masses are employed to constrain the CLDM further, and we find that they disfavor some of the $\chi \mathrm{EFT}$ Hamiltonians. The CLDM allows us to study the complex interplay between bulk, surface, curvature, and Coulomb contributions, and their impact on the NS crust. It also reveals how the curvature energy alters the correlation between the surface energy and the bulk symmetry energy. Our analysis quantifies how the uncertainties associated with the EOS of homogeneous matter implies significant uncertainties for the composition of the crust, its proton fraction, and the volume fraction occupied by nuclei. We find that the finite-size effects impact the crust composition but have a negligible effect on the net isospin asymmetry of matter. The isospin asymmetry is largely determined by the bulk properties and the isospin dependence of the surface energy. The most significant uncertainties associated with matter properties in the densest regions of the crust, the precise location of the crust-core transition, are found to be strongly correlated with uncertainties associated with the Hamiltonians. By adopting a unified model to describe the crust and the core of NSs, we tighten the correlation between their global properties such as their mass-radius relationship, moment of inertia, crust thickness, and tidal deformability with uncertainties associated with the nuclear Hamiltonians.

We have extended the compressible liquid-drop model with a density-dependent surface term which allows for a unified description of both the nuclear ground-state energies and the incompressibility modulus in finite nuclei $K_A$. We analyze the role of the nuclear empirical parameters, e.g., $K_{\mathrm{sat}}$, $Q_{\mathrm{sat}}$, $L_{\mathrm{sym}}$, and $K_{\mathrm{sym}}$, which contribute to the bulk properties, as well as the role of the finite-size contributions. For the bulk properties, the density and isospin dependencies of the nuclear incompressibility in infinite matter are characterized by introducing new empirical parameters, and two new constraints for the value of $K_{\mathrm{sym}}$ are suggested. For finite nuclei, we employ a Bayesian approach coupled to a Markov-Chain Monte Carlo exploration of the parameter space to confront the model predictions of $K_A$ in Zr, Sn, and Pb isotopes to the experimental data. We show that $Q_{\mathrm{sat}}\approx -950\pm 200\mathrm{MeV}$ describes the experimental measurements of $K_A$ in these isotopes. This value is different from those deduced from phenomenological nuclear energy density functionals, suggesting a possible explanation of their difficulty to accurately describe Zr, Sn, and Pb data all together. In addition we explore the impact of a fictitious measurement of the giant monopole resonance energy in ${}^{132}\mathrm{Sn}$. We show that this measurement, provided it is accurate enough, will allow us to better determine $K_{\mathrm{sym}}$ and $K_{\tau }$. Finally we explore the properties of the speed of sound around saturation density and show the important role of finite-size terms in finite nuclei since they reduce the speed of sound to approximately half compared with nuclear matter.