Time Evolution as a Gauge Transformation: x^5-dependent Cosmological Solution in 5d Kaluza-Klein Theory

TL;DR

This paper demonstrates that in 5d Kaluza-Klein cosmology, an evolving universe can be viewed as gauge equivalent to a static universe, highlighting the role of gauge transformations in cosmological evolution.

Contribution

It introduces a new x^5-dependent solution in 5d Kaluza-Klein theory that links evolving and static universes through gauge transformations.

Findings

Evolving and static universes are gauge equivalent in this framework.

The solution extends Schwarzschild and relates to radiation-dominated cosmology.

Gauge choice determines the perceived evolution of the universe.

Abstract

We discuss a new feature of the 5d Kaluza-Klein cosmology. For that purpose, we obtain the simplest x^5-dependent solution which, in the reduced description, is associated with a radiation-dominated Robertson-Walker universe, and also can be regarded as an extension of the Schwarzschild solution. This solution enables us to deduce an important result that an evolving universe is related with a static universe by the gauge transformation, i.e., they are gauge equivalent. This means that having a different universe simply corresponds to choosing a different gauge