The theoretical description of neutron stars, relevant to the interpretation of a variety of astrophysical observations, requires a quantitative understanding of both equilibrium and non equilibrium properties of nuclear matter at high density. However, while equilibrium properties---e.g. the zero-temperature equation of state (EOS)---are generally obtained from realistic dynamical models, strongly constrained from nuclear systematics and nucleon-nucleon scattering data, theoretical studies of the dynamical properties, such as the response functions, often resort to oversimplified models of nuclear interactions.

The work aimed at developing a consistent description of the nuclear matter EOS and electroweak response in the low-energy region, carried out by my group over the past decade, has been largely based on a density-dependent effective interaction, derived from a highly realistic nuclear hamiltonian using the formalism of correlated basis functions (CBF) and the cluster expansion technique [Phys. Rev. Lett. 99 (2007) 232501; Phys. Rev. C 83 (2011) 054003].

By construction, the CBF effective interaction provides the same EOS obtained from state-of-the-art ab initio approaches, such as Fermi Hyper-Netted Chain (FHNC) and Green's Function Monte Carlo (GFMC). However, unlike the bare nucleon-nucleon potential, it is suitable to carry out perturbative calculations of a variety of nuclear matter properties, including the dynamic responses, using the basis states of the non interacting system.

The calculated responses to neutral current weak interactions with neutrinos carrying energies of few MeV have been used to obtain the corresponding contributions to the neutrino mean free path in both pure neutron matter and isospin-symmetric matter at zero temperature [Phys. Rev. C 89 (2014) 025804].

In addition, combining the effective interaction formalism to Landau's theory of normal Fermi liquids we have been able to extend its applicability to the regime of non vanishing temperature, relevant to supernovae and newly formed neutron stars [Phys. Rev. C 87 (2013) 014601].

In the past few years, the CBF efective interactions has been employed to carry out systematic calculations of the equation of state of nuclear matter with arbitrary neutron excess and nonzero temperature [Phys. Rev. C 96 (2017) 054301]. The fisrt results of this work have been employed to study the neutrino luminosity and gravitational wave emission of protoneutron stars during the Kelvin-Helmoltz evolutionary phase [Phys. Rev. D 96 (2017) 043015].