  We use the 3+1 formalism of numerical relativity to investigate the
robustness of Starobinsky and Higgs inflation to inhomogeneous initial
conditions, in the form of either field gradient or kinetic energy density.
Sub-Hubble and Hubble-sized fluctuations generically lead to inflation after an
oscillatory phase between gradient and kinetic energies. Hubble-sized
inhomogeneities also produce contracting regions that may end up forming
primordial black holes, subsequently diluted by inflation. We analyse the
dynamics of the preinflation era and the generation of vector and tensor
fluctuations. Our analysis further supports the robustness of inflation to any
size of inhomogeneity, in the field, velocity or equation of state. At large
field values, the preinflation dynamics only marginally depends on the field
potential and it is expected that such behaviour is universal and applies to
any inflation potential of plateau-type, favoured by CMB observations after
Planck.
