Constraining gravity theories with neutron star mass-radius observations, or not

The structure of a compact object in an alternative theory is different from the case in general relativity (GR), hence any measurement of these structures can, in principle, be used to test deviations from GR. A recent concrete example is the spontaneous scalarization scenario of Damour and Esposito-Farese (DEF), where part of the parameter space has been ruled out via Bayesian inference by comparing the simultaneous mass and radius measurements of neutron stars with theoretical predictions. Here, we extend this work to generalizations of the DEF model as well as the scalar-Gauss-Bonnet theories which are known to feature spontaneous scalarization. We find that, unlike the original DEF model, the current mass-radius data set does not provide significant constraints in these cases. This is sometimes due to the fact that the theory closely resembles GR, and sometimes due to uncertainties in the data and modeling. We discuss how these results can and cannot be improved with future observations, and plans to adapt the same method to other alternative theories of gravitation.