Gravitational Higgs mechanism and resulting observational effects

Recently, a toy model was introduced to demonstrate that screening mechanisms in alternative theories of gravitation can hide additional effects. In this model a scalar field is charged under a U(1) symmetry. In sufficiently compact objects the scalar field spontaneously grows, i.e., the object scalarizes, spontaneously breaking the U(1) symmetry. Exactly as in the U(1) Higgs mechanism this leads to the emergence of a mass for the gauge field. The aim of this paper is to provide an example of the physical consequences if we consider this toy model as a prototype of Weak Equivalence Principle (WEP) violations. We model neutron stars with a dipolar magnetic field to compare the magnetic field behavior of stars in Einstein-Maxwell theory on the one hand and in scalar-tensor theory with the, so-called, gravitational Higgs mechanism on the other hand.