Systematic errors due to quasi-universal relations in binary neutron stars and their correction for unbiased model selection

Inference of the equation-of-state (EoS) of dense nuclear matter in neutron-star cores is a principal science goal of X-ray and gravitational-wave observations of neutron stars. In particular, gravitational-wave observations provide an independent probe of the properties of bulk matter in neutron star cores that can then be used to compare with theoretically derived equations of state. In this paper, we quantify the systematic errors arising from the application of EoS-independent \emph{quasi-universal relations} in the estimation of neutron star tidal deformabilities and radii from gravitational-wave measurements and introduce a strategy to correct for the systematic biases in the inferred radii. We apply this method to a simulated population of events expected to be observed by future upgrades of current detectors and the next-generation of ground-based observatories. We show that our approach can accurately correct for the systematic biases arising from approximate universal relations in the mass-radius curves of neutron stars. Using the posterior distributions of the mass and radius for the simulated population we infer the underlying EoS with a good degree of precision. Our method revives the possibility of using the universal relations for rapid Bayesian model selection of dense matter EoS in gravitational-wave observations.