Five-Dimensional Cosmological Model with Variable G and Λ

Einstein's field equations with G and Λ both varying with time are considered in the presence of a perfect fluid for five-dimensional cosmological model in a way which conserves the energy momentum tensor of the matter content. Several sets of explicit solutions in the five-dimensional Kaluza--Klein type
cosmological models with variable G and Λ are obtained. The diminishment of extra dimension with the evolution of the universe for the five-dimensional model is exhibited. The physical properties of the models are examined.