Bayesian investigation of the neutron star equation of state vs gravity degeneracy

Despite its elegance, the theory of General Relativity (GR) is subject to experimental, observational, and theoretical scrutiny to arrive at tighter constraints or an alternative, more preferred theory. In alternative gravity theories, the macroscopic properties of neutron stars, such as mass, radius, tidal deformability, etc. are modified. This creates a degeneracy between the uncertainties in the equation of state (EOS) and gravity since assuming a different EOS can be mimicked by changing to a different theory of gravity. We formulate a hierarchical Bayesian framework to simultaneously infer the EOS and gravity parameters by combining multiple astrophysical observations. We test this framework for a particular 4D Horndeski scalar-tensor theory originating from higher-dimensional Einstein-Gauss-Bonnet gravity and a set of 20 realistic EOSs and place improved constraints on the coupling constant of the theory with current observations (still inferred assuming General Relativity). Assuming a large number of observations with upgraded or third-generation detectors, we find that the $A+$ upgrade could place interesting bounds on the coupling constant of the theory, whereas with the LIGO Voyager upgrade or the third-generation detectors (Einstein Telescope and Cosmic Explorer), the degeneracy between EOS and gravity could be resolved with high confidence, even for small deviations from GR.

Figure 1

Representative mass vs radius sequences for different values of the coupling constant $\alpha [{\mathrm{km}}^2]$ using the SLY4 EOS.

Figure 2

Mass vs radius for sequences of nonrotating equilibrium models in GR for all the 20 EOSs considered in this study.

Figure 3

Marginalized posterior distribution of $\alpha$ obtained using current astrophysical observations under the assumption of three different NS mass population models. For each model, the corresponding median and 90% CI are also indicated using solid and dashed lines in the same color, respectively.

Figure 4

Left panel: the uncertainty in radius as a function of mass in the $[1.0,1.6]M_{\odot }$ range at three different detector sensitivity levels. In this example, the injected EOS is SLY4 with $\alpha =0.05$. Right panel: mass vs radius sequences for the different injected values of $\alpha$ (the GR case corresponds to $\alpha =0$).

Figure 5

Recovered posteriors of the coupling constant $\alpha$ at $\mathrm{A}+$, Voyager, and 3G sensitivity levels (left, middle, and right columns, respectively), for injections with the SLY4 EOS and $\alpha =[0.05,1,5]$ (top, middle, and last rows, respectively). For each posterior of $\alpha$, the median and $1\sigma$ CI are quoted at the top and also shown by the dashed vertical lines. In the case of Voyager and 3G, only the SLY4 EOS is recovered. In the case of $\mathrm{A}+$, the posterior distribution of $\alpha$ also includes a secondary peak corresponding to the SFHO EOS. Nevertheless, for an injection of $\alpha =5{\mathrm{km}}^2$, the posterior distribution excludes the GR value of $\alpha =0$ at the $3\sigma$ level.