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.