Infinity of Geodesics in an Homogeneous and Isotropic Expanding Space-Time

TL;DR

This paper models an expanding homogeneous and isotropic space-time using a discrete simulation, revealing that geodesics are curved and fluctuate, leading to infinite possible paths and implications for cosmic polarization and early acceleration.

Contribution

It introduces a novel discrete simulation approach to analyze space-time expansion, demonstrating fluctuating geodesics and their physical implications.

Findings

Geodesics fluctuate on boundaries of expanding elements

Infinite geodesic paths exist between any two points

Predicts polarization effects and early universe acceleration

Abstract

In this paper we construct a discrete simulation of an expanding homogeneous and isotropic space-time that expands via expansion of its basic elements to figure out properties and characteristics of such a space-time and derive conclusions. We prove that in such an expanding space-time, the geodesics are curved and more precisely, they fluctuate on the boundaries of the expanding basic elements. The non existence of privileged expansion direction leads to the existence of an infinity of fluctuating geodesics between any two locations in this space-time, that provides a prediction of polarization in geometric optics, and a prediction of an earlier acceleration of the expansion as for the cosmic inflation model. This simulation is a case study and an example of space-time with variable topology using the principle of variation of topology via a transformation that creates holes.