Oscillating universes as eigensolutions of cosmological Schr\"odinger equation

TL;DR

This paper introduces a cosmological model that explains the universe's periodic structures by reducing the Einstein equations to a Schr"odinger-like equation, with oscillating solutions accounting for observed galaxy cluster patterns.

Contribution

It presents a novel approach by formulating cosmological dynamics as a Schr"odinger equation, providing a natural explanation for large-scale periodicity in the universe.

Findings

Periodic structures can be modeled as eigensolutions of a Schr"odinger-like equation.

The model aligns with observed galaxy cluster distributions.

Oscillating solutions correspond to large-scale universe patterns.

Abstract

We propose a cosmological model which could explain, in a very natural way, the apparently periodic structures of the universe, as revealed in a series of recent observations. Our point of view is to reduce the cosmological Friedman--Einstein dynamical system to a sort of Schr\"odinger equation whose bound eigensolutions are oscillating functions. Taking into account the cosmological expansion, the large scale periodic structure could be easily recovered considering the amplitudes and the correlation lengths of the galaxy clusters.