International Journal of Research in Advent Technology, Vol.8, No.1, January 2020 E-ISSN: 2321-9637 Available online at www.ijrat.org 10 doi: 10.32622/ijrat.81202012 Abstract— In this present study we have investigated Kantowski-Sachs universe filled with perfect fluid and radiation with a cosmological constant. To get determinate solution, it is assumed that the shear scalar is proportional to s scalar of expansion hear scalar, which yields the relation between metric potentials as n S A R = . The cosmological parameters of models are also discussed. Index Terms— Perfect fluid, Radiation, cosmological constant, Kantowski-Sachs space-time I. INTRODUCTION The spatially homogeneous and anisotropic Kantowski-Sachs model has astro-physically important as it represent early era in cosmology. The recent observations indicate that the universe is expanding and on large scale it is homogeneous and isotropic (Knop et.al (2003), Gasprini (2003), Riess et.al. (2004)) and is in accelerating phase. Roy Choudhari (1979) have studied the solutions of homogeneous space-time belongs to either Bianchi types or Kantowski-Sachs in general relativity. Kantowski-Sachs models have been studied by Weber (1984, 85), Lorcaz (1983), Gron (1986), Matravers (1988), Krori et.al.(1995), Li & Hao (2003). Sing and Agrawal have analyzed Kantowski-Sachs model in Seaz Ballester (1985) and scalar tensor theory (1991). Pradhan and Yadav (2002) have obtained the solutions for Kantowski-Sachs model with variable G and . Anisotropic dark energy model has been investigated and studied by Adhav et.al. (2011) in Kantowski-Sachs space-tine. To understand the early and present stages of the universe, the FRW models are considered as standard cosmological models. Many authors investigated two fluid FRW models (Davidson 1962; McIntosh 1968). Two fluid models where one fluid is the radiation corresponding to the observed cosmic background radiation, while the matter content of the universe is represented by perfect fluid have studied by Coley and Tupper (1986) and Coley (1988). An interacting two fluid FRW universe is investigated by Pradhan et.al. (2011). Two fluid anisotropic cosmological models have been studied by Coley and Dunn (1990), Pant and Oli (2002), Oli (2008), Adhav et.al. (2011). Manuscript revised on January 25, 2020; and published on February 10, 2020 S. M. Botikar, Department of Applied Science, Sipna College of Engineering and Technology, Amravati, India. soniyanishant@gmail.com In this paper we assume that the geometry of the universe is that of a Kantowski-Sachs space-time. The solution of field equations is obtained and physical behavior of the corresponding non-interacting fluids model is discussed. II. METRIC AND BASIC FIELD EQUATIONS The Kantowski-Sachs space-time is given by ) sin ( 2 2 2 2 2 2 2 2    d d S dr R dt ds + − − = , (1) Where R and S are scale factors and are functions of time t only. The Einstein field equations are (For 1 , 1 8 = = c G  ) given by ) ( 2 1 ) ( ) ( r j i m j i j i j i T T R R + − =  + −  , (2) Where j i R is the Ricci tensor, R is the Ricci scalar and ) ( m j i T and ) ( r j i T are the energy momentum tensor for matter(perfect fluid) and radiation field respectively and  is a cosmological constant. The energy-momentum tensors for matter (perfect fluid) and radiation are given by m j i m m m j i p u u p T − + = ) ( ) (  , r j i r r j i u u T   3 1 3 4 ) ( − = ; (3) with components m m m m m m T p T T T  = − = = = ) ( 0 0 ) ( 3 3 ) ( 2 2 ) ( 1 1 , , r r r r r r T T T T   = − = = = ) ( 0 0 ) ( 3 3 ) ( 2 2 ) ( 1 1 , 3 (4) where m m p  , and r  are pressure and densities of matter and radiation respectively. Einstein’s field equations (2) for line element (1) and with the equation (4) are Dynamics of Non-Interacting Fluids in Kantowski-Sachs Universe with a Cosmological Constant S. M. Borikar