Oscillating Friedman Cosmology

TL;DR

This paper explores a non-singular, oscillating Friedmann cosmology within General Relativity, identifying conditions for oscillations, their potential to support standard universe processes, and implications for dark matter candidates.

Contribution

It provides a detailed analysis of oscillatory solutions in Friedmann cosmology, including conditions for their existence and interpretations involving scalar fields and dark matter.

Findings

Oscillations require wall-like matter and a small negative cosmological constant.

Oscillations can be deep enough for recombination and nucleosynthesis.

Scalar fields with oscillating potentials can model dark matter.

Abstract

The non-singular, oscillating Friedman cosmology within the framework of General Relativity is considered. The general oscillatory solution given in terms of elliptic functions and the conditions for its existence are discussed. It is shown that the wall-like-matter and the small, but negative cosmological constant are required for oscillations. The oscillations can , in principle, be deep enough to allow standard hot universe processes like recombination and nucleosynthesis. It is shown that the wall-like-matter and string-like-matter can be interpreted as scalar fields with some potentials. This may give another candidate for the dark matter which may be compatible with observational data. For an exact elementary oscillatory solution it is shown that the associated scalar field potential is oscillating as well.