  Binary pulsar observations and gravitational wave detections seriously
constrained scalar-tensor theories with massless scalar field allowing only
small deviations from general relativity. If we consider a nonzero mass of the
scalar field, though, significant deviations from general relativity are
allowed for values of the parameters that are in agreement with the
observations. In the present paper we extend this idea and we study
scalar-tensor theory with massive field with self-interaction term in the
potential. The additional term suppresses the scalar field in the neutron star
models in addition to the effect of the mass of the scalar field but still,
large deviations from pure GR can be observed for values of the parameters that
are in agreement with the observations.
