The Regular Universe

TL;DR

This paper proposes a singularity-free, cyclic cosmological model where the universe's radius oscillates periodically, utilizing dark matter as a tensor field to ensure regularity and derive key cosmological equations.

Contribution

It introduces a novel regular universe model based on a periodic radius function and dark matter as a compensational tensor field, avoiding singularities.

Findings

Universe radius is a simple periodic function of cosmic time.

Dark matter is modeled as a tensor field for regularity.

Derived equations for pressure, energy, and momentum compensons.

Abstract

A regular (i.e., singularity-free) cycling cosmological model is advanced. In the model, there are only two constants: the gravitational constant (or the Planck time) and the cosmic period. The radius of the universe is a simple periodic function of cosmic time. The regularity of the construction is achieved via the condition that the measure associated with metric be the Haar measure on the 3-space. The possibility of the construction is due to dark matter---as long as it is treated not as a particle matter, but as a compensational tensor field. The metrodynamical equation, i.e., an equation for metric, is derived and expressions for the pressure, energy and momentum compensons are obtained.