General Analytical Conditions for Inflaton Fragmentation: Quick and Easy
  Tests for its Occurrence
  Understanding the physics of inflaton condensate fragmentation in the early
Universe is crucial as the existence of fragments in the form of
non-topological solitons (oscillons or Q-balls) may potentially modify the
evolution of the post-inflation Universe. Furthermore, such fragments may
evolve into primordial black holes and form dark matter, or emit gravitational
waves. Due to the non-perturbative and non-linear nature of the dynamics, most
of the studies rely on numerical lattice simulations. Numerical simulations of
condensate fragmentation are, however, challenging and, without knowing where
to look in the parameter space, they are likely to be time-consuming as well.
In this paper, we provide generic analytical conditions for the perturbations
of an inflaton condensate to undergo growth to non-linearity in the cases of
both symmetric and asymmetric inflaton potentials. We apply the conditions to
various inflation models and demonstrate that our results are in good agreement
with explicit numerical simulations. Our analytical conditions are easy to use
and may be utilised in order to quickly identify models that may undergo
fragmentation and determine the conditions under which they do so, which can
guide subsequent in-depth numerical analyses.
