Nuclear Physics and Astrophysics Constraints on the High Density Matter Equation of State

(1) This review has been written in memory of Steven Moszkowski who unexpectedly passed away in December 2020. It has been inspired by our many years of discussions. Steven's enthusiasm, drive and determination to understand atomic nuclei in simple terms of basic laws of physics was infectious. He sought the fundamental origin of nuclear forces in free space, and their saturation and modification in nuclear medium. His untimely departure left our job unfinished but his legacy lives on. (2) Focusing on the nuclear force acting in nuclear matter of astrophysical interest and its equation of state (EoS), we take several typical snapshots of evolution of the theory of nuclear forces. We start from original ideas in the 1930s moving through to its overwhelming diversity today. The development is supported by modern observational and terrestrial data and their inference in the multimessenger era, as well as by novel mathematical techniques and computer power. (3) We find that, despite the admirable effort both in theory and measurement, we are facing multiple models dependent on a large number of variable correlated parameters which cannot be constrained by data, which are not yet accurate, nor sensitive enough, to identify the theory closest to reality. The role of microphysics in the theories is severely limited or neglected, mostly deemed to be too difficult to tackle. (4) Taking the EoS of high-density matter as an example, we propose to develop models, based, as much as currently possible, on the microphysics of the nuclear force, with a minimal set of parameters, chosen under clear physical guidance. Still somewhat phenomenological, such models could pave the way to realistic predictions, not tracing the measurement, but leading it.