The mass of the dominant particle in a fractal universe

TL;DR

This paper develops a fractal scaling law model to estimate the dominant particle's mass in galaxies, suggesting it is near the nucleon mass and related to the cosmological constant.

Contribution

It generalizes an empirical model using fractal laws to determine the dominant particle mass in galaxies, linking it to fractal dimension and cosmological parameters.

Findings

Dominant particle mass ranges between Planck mass and 1 eV for fractal dimensions 1-3.

Fractal dimension near 2 aligns with the nucleon mass for the dominant particle.

Particle mass is proportional to the sixth root of the cosmological constant.

Abstract

An empirically validated, phenomenological model relating the parameters of an astronomical body to the stochastic fluctuations of its granular components is generalized in terms of fractal scaling laws. The mass of the particle constituting the preponderance of the mass of a typical galaxy is determined from the generalized model as a function of the fractal dimension. For a fractal dimension between 1 and 3 the mass of the dominant particle in galaxies is, roughly, between the Planck mass and 1eV. If the dimension is near 2 then the fractal model is identical to the original stochastic model, and the mass of the dominant particle must be of order near the nucleon mass. Two additional expressions for the mass of the dominant particle in the universe are obtained from basic quantum considerations and from the existence of a cosmological constant. It follows that the fractal dimension 2 is favored and that the mass of the dominant particle is proportional to sixth root of the cosmological constant and of order near the nucleon mass.