  We study the non-perturbative evolution of inflationary fluctuations during
preheating using fully non-linear general-relativistic field-theory
simulations. We choose a single-field inflationary model that is consistent
with observational constraints and start the simulations at the end of
inflation with fluctuations both in the field and its conjugate momentum.
Gravity enhances the growth of density perturbations, which then collapse and
virialize, forming long-lived stable oscillon-like stars that reach
compactnesses $\mathcal{C}\equiv GM/R \sim 10^{-3}-10^{-2}$. We find that
$\mathcal{C}$ increases for larger field models, until it peaks due to the
interplay between the overdensity growth and Hubble expansion rates. Whilst
gravitational effects can play an important role in the formation of compact
oscillons during preheating, the objects are unlikely to collapse into
primordial black holes without an additional enhancement of the initial
inflationary fluctuations.
