Oscillons of axion-like particle: mass distribution and power spectrum

In string theory, the simultaneous existence of many Axion-Like Particles (ALPs) are suggested over a vast mass range, and variety potentials have been developed in context inflation. such shallower than quadratic, prominent instability can produce localized dense objects, oscillons. Because approximate conservation their adiabatic invariant, oscillons generally survive quite long, maybe up to current age universe case ultra-light ALPs with m ∼ 10−22 eV. Such significant effects on evolution recent universe. this paper, we investigate pure-natural type potential by classical lattice simulation explore key quantities necessary for phenomenological application: number density oscillons, oscillon distribution, energy ratio ALP field, power spectrum. Then, evolve these values consideration analytic decay rate.