Quasiuniversal relations in the context of future neutron star detections

The equation of state dependence of a neutron star's astrophysical features is key to our understanding of isospin asymmetric and dense matter. There exists a series of almost equation of state independent relations reported in the literature, called quasiuniversal relations, that are used to determine neutron star radii and moments of inertia from x-ray and gravitational wave signals. Using sets of equations of state constrained by multimessenger astronomy measurements and nuclear-physics theory, we discuss quasiuniversal relations in the context of future gravitational wave detectors Cosmic Explorer and Einstein Telescope, and the Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays.. We focus on relations that involve the moment of inertia $I$, the tidal deformability $\Lambda$, and the compactness $C$: $C\left(\Lambda \right)$, $I\left(\Lambda \right)$, and $I\left(C\right)$. The quasiuniversal fits and their associated errors are constructed with three different microphysics approaches which include state of the art nuclear physics theory and astrophysical constraints. Gravitational-wave and x-ray signals are simulated with the sensitivity of the next generation of detectors. Equation of state inference on those simulated signals is compared to determine if it will offer a better precision on the extraction of a neutron star's macroscopic parameters than quasiuniversal relations. We confirm that the relation $I\left(\Lambda \right)$ offers a more pronounced universality than relations involving the compactness regardless of the equation of state set. We show that detections with the third generation of gravitational wave detectors and future x-ray detectors will be sensitive to the fit error marginalization technique. We also find that the sensitivity of those detectors will be sufficient in that using full equation of state distributions leads to significantly better precision on extracted parameters than quasiuniversal relations. We also note that nuclear physics theory offers a more pronounced equation of state invariance of quasiuniversal relations than current astrophysical constraints.