Theory and observation of spontaneous scalarization

Spontaneous scalarization is a scenario within scalar-tensor theories of gravity which allows stellar structures to deviate significantly from general relativity in the fairly less understood strong gravity regime. Even though this can be achieved in many alternative theories, scalarization also provides observables that closely mimic general relativity for weak fields, hence it naturally passes all the classical tests of gravity. In this thesis, we will first discuss the original model of spontaneous scalarization by Damour and Esposito-Far\`{e}se which allows neutron stars to scalarize. Then, we will see how experimental observations rule out much of the parameter space of this idea, and how giving the scalar field a mass can avoid such constraints, rendering the theory viable once again. Next, we will explore the more recent models of spontaneous scalarization which allow both black holes and neutron stars to scalarize. Finally, we will present the recent idea of constraining all models of spontaneous scalarization using neutron star mass-radius measurements. All the aforementioned efforts require numerical computation of the scalarized astrophysical objects under spontaneous scalarization, and comparison of the theoretical results to the observations. Hence, in the final parts of our thesis, we will explain the numerical and statistical methods that have been developed to tackle these issues.