IJREAS VOLUME 5, ISSUE 8 (August, 2015) (ISSN 2249-3905) International Journal of Research in Engineering and Applied Sciences (IMPACT FACTOR – 5.981) International Journal of Research in Engineering & Applied Sciences Email:- editorijrim@gmail.com, http://www.euroasiapub.org 12 Higher Dimensional Kaluza-Klein Cosmological Model with Time Dependent G and  term in General Relativity Kalpana Pawar (Mody) 1 , Department of Mathematics, Shri R.R. Lahoti Science College, Morshi, Affiliated to SGB Amravati University, Amravati, India Rishikumar Agrawal 2 Department of Mathematics, Hislop College, Affiliated to RTM Nagpur University, Nagpur, India. ABSTRACT In this paper we have obtained the exact solution of Einstein's field equations with time dependent gravitational and cosmological constant term in the presence of perfect fluid for the five dimensional Kaluza-Klein space-time. The nature of G(t) and ฀ ȋtȌ have been examined for two different cases, it is observed that due to the combined effect of time dependent ฀ ฀ and G the universe evolved with decelaration as well as accelaration. We also obtain the value of scalar expansion ฀ , shear tensor ฀ij and the Hubbles parameter H. Moreover it is observed that for this model G varies with time as suggested by large number hypothesis proposed by Dirac. Some physical and geometrical properties of the model are discussed which are in good agreement with the observational results. Keywords: Cosmology, exact solution, five dimension, perfect fluid and G(t), ฀ ȋtȌ. 1. Introduction The Einstein field equation has two parameters, the gravitational constant G and the cosmological constant ฀. The Newtonian constant of gravitation G plays the role of a coupling constant between geometry and matter in the Einstein field equation. In an evolving universe, it appears to look at this constant as a function of time. There are significant observational evidence that the expansion of the Universe is undergoing a late time acceleration. This, in other words, amounts to saying that in the context of Einstein’s general theory of relativity some sort of dark energy, constant or that varies only slowly with time and space dominates the current composition of cosmos. The origin and nature of such an accelerating field poses a completely open question. The exact physical situation at very early stages of the formation of our universe provoked great interest among researchers. Higher dimensional space- time has taken considerable research interest in an attempt to unify gravity with other forces in nature. This idea is particularly important in the field of cosmology since one knows that our universe was much smaller in its early stage than it is today. In this connection a number of attempts have been made to study the role of gravity with other fundamental forces in nature.