COSMOLOGICAL SOLUTIONS AND THEIR EFFECTIVE PROPERTIES OF MATTER IN KALUZA-KLEIN THEORY

We derive a ''wave-like'' class of exact cosmological solutions of the apparently empty 5D Kaluza-Klein field equations. Here by ''wave-like '' we mean that the solutions look like plane waves propagating in the fifth dimension. In the interpretation that the fifth dimension in Ka luza-Klein theory may induce matter in four dimensions, we then calcul ate the effective energy density rho and pressure p, and study in deta il the case for which the equation of state is p = gamma rho (where ga mma is an arbitrary constant). We show that for both the matter-domina ted (gamma = 0) and radiation-dominated (gamma = 1/3) eras of the univ erse, the 4D spacetime defined by hypersurfaces of the 5D metrics are just the same as those of the standard Friedmann-Robertson-Walker mode ls of general relativity. However, in our models the big bang is like a shock wave propagating along the fifth dimension, and different obse rvers can measure different ages for the universe. This property may b e tested using the spread in ages of astrophysical objects such as glo bular clusters.