Studies of the Inhomogeneous Cosmology in Higher Dimensional space-time with a Cosmological Constant

Abstract

We have studied the inhomogeneous cosmology in Kaluza-Klein spacetime with a positive cosmological constant in a dust dominated era ($p = 0$). Depending on the integration constant we have derived two types of solutions. The dimensional reduction of extra dimensional scale factor is possible due to inhomogeneity depending on the curvature of the metric for positive cosmological constant for all solutions. The high value of entropy in present observable universe and the possible matter leakage in $4D$ world due to reduction of extra dimension are also discussed. Our solutions show the early deceleration and late accelerating nature of the universe. Findings are verified by the wellknown Raychaudhuri equation.