International Journal of Physics and Mathematical Sciences ISSN: 2277-2111 (Online) An Online International Journal Available at http://www.cibtech.org/jpms.htm 2012 Vol. 2 (1) January-March, pp.148-156/ Dubey et al. Research Article 148 AN QUALITATIVE STUDY OF ANISOTROPIC BIANCHI TYPE-II COSMOLOGICAL MODELS WITH VARYING COSMOLOGICAL TERM *R. K. Dubey 1 , Bijendra Kumar Singh 2 and Abhijeet Mitra 3 1 Department of Mathematics, Govt. Science P.G.College, Rewa, Madhya Pradesh, India 2 Department of Mathematics, Govt. P G College, Satna, Madhya Pradesh, India 3 Department of Mathematics, Govt. P G College, Satna, Madhya Pradesh, India *Author for Correspondence ABSTRACT Einstein’s field equations are considered for a Bianchi type-II space time with time- decaying cosmological term ) ( t . Applying a special law of variation for Hubble’s parameter exact solutions of field equations are obtained. An anisotropic cosmological model with a negative constant deceleration parameter is presented for accelerated phase of universe. Kinematic properties and behavior of the models has been discussed. INTRODUCTION Evolution of universe has been investigated in general relativistic cosmological models. Our present cosmology is based on Friedmann-Robertson-Walker (FRW) model. For simplification and description of the large scale behavior of the actual universe, locally rotationally symmetric Bianchi type-II space time has been studied. In FRW cosmological model, the universe is completely homogeneous and isotropic which is agreed by the observational data about the large scale structure of the universe. Experimental studies of the isotropy done by cosmic microwave background radiation and speculation about the amount of the helium formed at the early stage of the evolution of universe have stimulated theoretical interest in an anisotropic cosmological model. Recent experimental data and critical arguments support the existence of an anisotropic phase of the cosmic expansion that approaches an isotropic one. This results for exact anisotropic solution of Einstein‘s field equations for cosmological models for universe. Bianchi type-II cosmological models are important for constructing models with geometrical and physical structure for describing the early stages of evolution of universe. Asseo and Sol (1987) describes the importance of Bianchi type-II cosmological models. Lorenz (1980) has presented exact solutions for rotationally symmetric Bianchi type-II space time stiff matter models in an electromagnetic field theory. Exact solutions to Einstein‘s field equations for locally rotationally symmetric Bianchi type-II cosmological models was obtained by Hajj-Boutors (1986). For perfect fluid of matter, Shanthi and Rao (1991), presented Bianchi type II model in Barber’s self creation theory of gravitation. Cosmological solution of Bianchi type II stiff fluid models using electromagnetic field was obtained by Venkateswarlu and Reddy (1991). Bianchi type II inflationary model with constant deceleration parameter was derived by Singh and Kumar (2007). One of the most important and outstanding problems in cosmology is the cosmological constant and gravitational constant. Recent observations by Perlmutter et al. (1998,1999) and Riess et al. (1998) strongly favour a significant and positive value of . Al.Rawaf and Taha and Al-Rawaf (1998) and Overdin and Cooperstock (1998) proposed a cosmological model with a cosmological constant of the form 1 1 a a   , where 1 a is scale factor of universe and is a constant. Recently, Pradhan et al. (2008) have shown that spatially homogeneous Bianchi type II cosmological model with stiff matter and time decaying term is compatible with recent observations on accelerated universe. One of the