Spontaneous scalarization for non-minimally coupled self-interacting scalars

Modified gravity theories in which a scalar field is non-minimally coupled to the Ricci scalar can exhibit a behaviour called "spontaneous scalarization". This phenomenon is a strong-field phase transition that allows the scalar field to be non-linearly quenched into a scalar-hairy configuration, which can be constrained observationally. Here, we investigate scalarization for theories with relevance in cosmology. As a representative case, we choose a scalar field non-minimally coupled to the Ricci scalar with a double-well potential. This Lagrangian is used in a variety of different cosmological theories, from Higgs inflation to Early Modified Gravity. In particular, we have searched for strong gravity effects around dense compact objects that have detached from the cosmological expansion. We have developed a numerical algorithm to solve the Einstein and Klein-Gordon equations in the Jordan frame, in a static spherically symmetric spacetime. We have performed perturbative expansions to determine the initial conditions and the conserved quantities of the system. This allowed us to integrate the TOV+scalar system of equations and obtain results across the parameter space. The code was first tested in GR, obtaining an agreement at the percent level, and then we compared some results with known scalar-tensor theories in the literature, obtaining the same level of agreement. We have found spontaneous scalarization for different values of the parameters and studied their interplay with the cosmological constraints, therefore bridging the weak and strong gravity regimes for this scalar-tensor gravity model.