Time evolution as a gauge transformation: x5-dependent cosmological solution in 5d Kaluza–Klein theory

We discuss a new feature of the 5d Kaluza–Klein cosmology. For that purpose, we obtain the simplest x5-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.