Gravitational memory of boson stars

`Gravitational memory' refers to the possibility that, in cosmologies with a time-varying gravitational `constant', objects such as black holes may retain a memory of conditions at the time of their birth. We consider this phenomenon in a different physical scenario, where the objects under consideration are boson stars. We construct boson star solutions in scalar-tensor gravity theories, and consider their dependence on the asymptotic value of the gravitational strength. We then discuss several possible physical interpretations, including the concept of pure gravitational stellar evolution.