Neutron stars are perfect candidates to investigate the effects of a modified gravity theory, since the curvature effects are significant and more importantly, potentially testable. In most cases studied in the literature in the context of massive scalar-tensor theories, inflationary models were examined. The most important of scalar-tensor models is the Higgs model, which, depending on the values of the scalar field, can be approximated by different scalar potentials, one of which is the inflationary. Since it is not certain how large the values of the scalar field will be at the near vicinity and inside a neutron star, in this work we will answer the question, which potential form of the Higgs model is more appropriate in order for it to describe consistently a static neutron star. As we will show numerically, the non-inflationary Higgs potential, which is valid for certain values of the scalar field in the Jordan frame, leads to extremely large maximum neutron star masses; however, the model is not self-consistent, because the scalar field approximation used for the derivation of the potential, is violated both at the center and at the surface of the star. These results shows the uniqueness of the inflationary Higgs potential, since it is the only approximation for the Higgs model, that provides self-consistent results.
Towards a self-consistent relativistic model of the exterior gravitational field of rapidly rotating neutron stars