Unified study of nuclear physics and dark matter constraints through gravitational-wave observations of binary neutron star mergers

Understanding the properties of strongly interacting matter at extreme densities is a central problem in fundamental physics, with neutron star mergers offering a natural laboratory to probe this regime. However, the complexity of the merger process complicates the interpretation of the associated gravitational-wave and electromagnetic signals. This picture becomes even more complex in the potential scenario in which dark matter accumulates around and in neutron stars, altering their structure and the associated observables. In this work, we study synthetic gravitational-wave observations of binary neutron star mergers with next-generation detectors, investigating their potential to extract both nuclear physics and dark matter constraints. We also examine how the potential presence of fermionic, non-self-interacting dark matter inside neutron stars affects the inference of nuclear empirical parameters. We find that combining observations can tighten constraints on nuclear empirical parameters. However, the inferred values remain sensitive to systematic modeling biases and intrinsic degeneracies among the parameters. Conversely, our analysis reveals that for non-self-interacting fermionic dark matter at mass fractions below one percent, it will be unlikely to find decisive evidence for dark matter when analyzing gravitational-wave signals. Consequently, systematic biases in nuclear empirical parameter inference potentially resulting from such a dark matter component are expected to be negligible even for observations with next-generation gravitational-wave detectors.