Open Universe Model: Description by Mathieu Functions

TL;DR

This paper presents a cosmological model of the open Universe using Mathieu functions, linking the universe's evolution to oscillatory equations and aligning with the Big Bang scenario.

Contribution

It introduces a novel approach by modeling the open Universe with Mathieu functions, connecting cosmological dynamics to oscillatory mathematical equations.

Findings

Universe behavior aligns qualitatively with Big Bang scenario

Model reduces gravitational equations to Mathieu-type oscillations

Provides a new mathematical framework for open Universe models

Abstract

A model of the open Universe described by a conformally flat 4-metric is considered. The gravitational equations with a perfect Pascal fluid as a source are reduced to the nonlinear equation of oscillations. It is proposed to consider this equation as the Mathieu equation encompassing some cosmological models. It is shown that the behaviour of the Universe state function is in qualitative accordance with the Big Bang scenario.