Particle Creation in Higher Dimensional Space-time with Variable G and Λ

In this paper we consider higher dimensional FRW type cosmological models with time-varying gravitational constant G=G(t) and decaying vacuum energy Λ=Λ(t) in context of the open thermodynamical system of particle creation. The particle creation rate is determined by variable G and Λ. An Exact solution of the gravitational field equations is obtained by assuming the exact power-law solution of the scale factor of the universe. We evaluate the various cosmological parameters and discuss their physical significance in detail for radiation and matter-dominated phases of the universe. The solutions are also relevant for quintessence (accelerating) universe. We also discuss the relevance of the solutions for 5-dimensional Kaluza-Klein FRW type model with and without particle creation in radiation and matter-dominated phases as special case. We obtain the solution where the gravitational constant increases with time during no particle creation. The cosmological constant Λ, however, decreases with time in all the cases.