Physics lacks a confirmed description of dark matter, has yet to develop an adequate understanding of dark energy, and includes unverified conjectures regarding new elementary particles. This essay features modeling that addresses those problems and explains otherwise unexplained data. Our modeling starts from five bases – multipole expansions for the electromagnetic and gravitational fields associated with an object, the list of known elementary particles, some aspects of mathematics for isotropic harmonic oscillators, concordance cosmology, and a conjecture that the universe includes six isomers of most elementary particles. The multipole expansions – which have use in conjunction with Newtonian kinematics modeling, special relativity, and general relativity – lead to a catalog of kinematics properties such as charge, magnetic moment, mass, and repulsive gravitational pressure. The multipole expansions also point to all known elementary particles, some properties of those particles, and properties of some would-be elementary bosons and elementary fermions. The harmonic-oscillator mathematics points to Gauge symmetries regarding some elementary bosons. The would-be elementary fermions lack charge and would measure as dark matter. The conjecture regarding six isomers of most elementary particles rounds out and dominates our specification for dark matter. Five of the isomers form the basis for most dark matter. Our modeling explains ranges of observed ratios of dark matter effects to ordinary matter effects – for the universe, galaxy clusters, two sets of galaxies observed at high redshifts, three sets of galaxies observed at modest redshifts, and one type of depletion of cosmic microwave background radiation. Our description of repulsive gravitational pressure points toward resolution for tensions – between data and modeling – regarding the recent rate of expansion of the universe, resolution for possible tensions regarding large-scale clumping, and resolution for possible tensions regarding interactions between neighboring galaxies. Our work regarding gravity, dark matter, and elementary particles suggests characterizations for eras that might precede the inflationary epoch, a mechanism that might have produced baryon asymmetry, mechanisms that govern the rate of expansion of the universe, and insight about galaxy formation and evolution.

We suggest progress regarding the following six physics opportunities. List all elementary particles. Describe dark matter. Explain ratios of dark matter to ordinary matter. Explain eras in the history of the universe. Link properties of objects. Interrelate physics models. We use models based on Diophantine equations.

We try to solve three decades-old physics challenges. List all elementary particles. Describe dark matter. Describe mechanisms that govern the rate of expansion of the universe. We propose new modeling. The modeling uses extensions to harmonic oscillator mathematics. The modeling points to all known elementary particles. The modeling suggests new particles. Based on those results, we do the following. We explain observed ratios of dark matter amounts to ordinary matter amounts. We suggest details about galaxy formation. We suggest details about inflation. We suggest aspects regarding changes in the rate of expansion of the universe. We interrelate the masses of some elementary particles. We interrelate the strengths of electromagnetism and gravity. Our work seems to offer new insight regarding applications of harmonic oscillator mathematics. Our work seems to offer new insight regarding three branches of physics. The branches are elementary particles, astrophysics, and cosmology.

We develop and apply new physics theory. The theory suggests specific unfound elementary particles. The theory suggests specific constituents of dark matter. We apply those results. We explain ratios of dark matter amounts to ordinary matter amounts. We suggest details about galaxy formation. We suggest details about inflation. We suggest aspects regarding changes in the rate of expansion of the universe. The theory points to relationships between masses of elementary particles. We show a relationship between the strength of electromagnetism and the strength of gravity. The mathematics basis for matching known and suggesting new elementary particles extends mathematics for harmonic oscillators.