Particle Creation by a Simple Fractal in an Expanding Universe

Abstract

A method is developed to implement a fractal (specifically the Cantor set) into cosmology via the mass parameter of a scalar field. When implemented into an early universe setting this fractal mass can induce instabilities leading to an explosive particle production akin to reheating after inflation. A precise relation can be established between the exponential growth of the mode function induced by (post-inflationary) parametric resonant growth of scalar mode functions and the corresponding fractal growth. While generically, the growth is exponential in time, the modes near the edge of instabilities can exhibit a power-law enhancement in the momentum leading in some cases to a (nearly) scale invariant spectrum. A detailed analysis shows that scale invariant spectrum is limited to sub-Hubble and near-Hubble modes, such that the resonant and fractal spectra cannot be readily used to explain the origin of Universe’s large scale structure.