  We study phenomenological features and stability of boson stars in massless
and massive scalar-tensor theory of gravity with Damour-Esposito-Farese
coupling. This coupling between the tensor and scalar sectors of the theory
leads to a phenomenon called spontaneous scalarization, the onset of which we
investigate by numerically computing families of boson-star models using
shooting and relaxation algorithms. We systematically explore the effects of
the theory's coupling, the mass of the gravitational scalar and the choice of
the bosonic potential on the structure of weakly and strongly scalarized
solutions. Scalarized boson-star models share many common features with neutron
stars in the same scalar-tensor theory of gravity. In particular, scalarization
can result in boson stars with significantly larger radii and masses, which
tend to be energetically favored over their weakly or non-scalarized
counterparts. Overall, we find that boson stars are not quite as susceptible to
scalarization as neutron stars.
