  We investigate the importance of local gravity during preheating, the
non-linear dynamics that may be responsible for starting the process of
reheating the universe after inflation. We introduce three numerical methods
that study a simple preheating scenario while relaxing gravitational
assumptions, culminating in studying the process in full numerical relativity.
We confirm that perturbation theory is no longer valid when one considers modes
whose wavelengths are comparable to the size of the horizon at the end of
inflation; however, this breakdown does not necessarily lead to a breakdown of
the preheating process in non-linear gravity. For the specific model we test we
find no evidence for the creation of primordial black holes from the
instabilities in this model. Finally, we remark on the opportunity for future
numerical study of non-linear gravitational dynamics in the early universe.
