  The dynamical evolution of self-interacting scalars is of paramount
importance in cosmological settings, and can teach us about the content of
Einstein's equations. In flat space, nonlinear scalar field theories can give
rise to localized, non-singular, time-dependent, long-lived solutions called
{\it oscillons}. Here, we discuss the effects of gravity on the properties and
formation of these structures, described by a scalar field with a double well
potential. We show that oscillons continue to exist even when gravity is turned
on, and we conjecture that there exists a sequence of critical solutions with
infinite lifetime. Our results suggest that a new type of critical behavior
appears in this theory, characterized by modulations of the lifetime of the
oscillon around the scaling law and the modulations of the amplitude of the
critical solutions.
