Cosmological models in a Kaluza-Klein theory with variable rest mass

A general class of solutions is obtained for a homogeneous, spatially isotropic five-dimensional (5D) Kaluza-Klein theory with variable rest mass. These solutions generalize in the algebraic and physical sense the previously found solutions in the literature. The 4D spacetime sections of the solutions reduce to the Minkowski metric, K=0 Robertson-Walker metric with the equation of statep=np (p=pressure,n=constant sound speed,=energy density), and to the Robertson-Walker spacetime with steady-state metric. Some of the solutions, in different limits, show compactification of the fifth dimension. Some extensions of the model are discussed.