Gauge equivalent universes in 5d Kaluza-Klein theory

TL;DR

This paper investigates gauge equivalence of time-dependent cosmological solutions in 5d Kaluza-Klein theory, showing that within a certain time scale, different evolving universes are gauge equivalent, but this equivalence breaks down afterward.

Contribution

It demonstrates the conditions under which 4d cosmological solutions are gauge equivalent in 5d Kaluza-Klein theory, highlighting a time-dependent gauge equivalence.

Findings

Within time scale τ_c, any evolving 4d universe is gauge equivalent.

Outside τ_c, gauge equivalence no longer holds and evolution is determined by field equations.

Gauge equivalence depends on the topology and compactification radius.

Abstract

We examine in the framework of 5d Kaluza-Klein theory the gauge equivalence of $x^5$-dependent cosmological solutions each of which describes in the 4d sector an arbitrarily evolving isotropic, homogeneous universe with some pure gauge. We find that (1)within a certain time scale $\tau_c$ (which is characterized by the compactification radius $R_c$) any arbitrarily evolving 4d universe is allowed to exist by field equations, and these 4d universes with appropriate pure gauges are all gauge equivalent as long as they are of the same topology. (2)Outside $\tau_c$ the gauge equivalence disappears and the evolution of the universe is fixed by field equations.