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In string theory, the simultaneous existence of many Axion-Like Particles(ALPs) are suggested over a vast mass range, and a variety of potentials havebeen developed in the context of inflation. In such potentials shallower thanquadratic, the prominent instability can produce localized dense objects,oscillons. Because of the approximate conservation of their adiabaticinvariant, oscillons generally survive quite long, maybe up to the current ageof the universe in the case of ultra-light ALPs with $m \sim 10^{-22}\ {\rmeV}$. Such oscillons can have significant effects on the evolution of therecent universe. In this paper, we investigate the oscillons of thepure-natural type potential by classical lattice simulation to explore the keyquantities necessary for phenomenological application: the number density ofoscillons, the oscillon mass distribution, the energy ratio of oscillons to theALP field, and the power spectrum. Then, we evolve these values inconsideration of the analytic decay rate.

Oscillons of Axion-Like Particle: Mass distribution and power spectrum