Toward a Unified Understanding of the Dense Matter Equation of State

Efforts to understand the equation of state (EOS) of dense nuclear matter at supra-saturation densities have grown more sophisticated over the past decade, driven by a surge in high-precision data from both terrestrial experiments and astrophysical observations. While for the former, heavy-ion collisions (HIC) represent a unique opportunity to constraint the EOS in a controlled laboratory setting, the latter can be precisely probed thanks to the advent of multi-messenger astronomy (MMA). However, as we move away from our understanding drawn from individual sources and limited statistics to the era of precision physics with improved datasets, the need for a systematic way to combine them becomes clear. In this article, we trace the individual methods for extracting the EOS both for HIC and MMA. We then review the current state-of-the-art efforts to combine these individual information sources from Bayesian multi-source analysis, e.g., the Nuclear Physics and Multi-Messenger Astrophysics (NMMA) and Bayesian Analysis of Nuclear Dynamics (BAND) frameworks, and fully integrated EOS frameworks, i.e., the Modular Unified Solver for the Equation of State (MUSES) calculation engine. We highlight the scientific advances made possible by each step and outline the remaining challenges that must be addressed to build a coherent, predictive picture of dense nuclear matter across all relevant regimes.