Highly compact neutron stars and screening mechanisms. I. Equilibrium and stability

Abstract: Modified theories of gravity that offer viable models for dark energy often rely on mechanisms that screen their effects in high density environments. From this perspective, it would appear that, once solar system constraints are satisfied, these theories would predict a trivial phenomenology for (much denser) neutron stars. In this work we explore the fact that in scalar-tensor theories the scalar degree of freedom does not couple to the mass density alone, but to the trace of the energy-momentum tensor - which can increase and eventually change sign as density and pressure build up in the core of neutron stars -, and investigate whether there could be a partial unscreening of the scalar field inside the most compact stars found in Nature. For this purpose, we construct neutron star solutions with realistic equations of state in theories with screening mechanisms and study their stability under radial perturbations. In particular, we find that stable solutions with a unscreened core can exist in chameleon models, while for the environmentally-dependent dilaton model a wealth of new, scalarized equilibrium solutions are found, some of which can be stable.