ISSN 2320-5407 International Journal of Advanced Research (2014), Volume 2, Issue 6, 1103-1114 1103 Journal homepage:http://www.journalijar.com INTERNATIONAL JOURNAL OF ADVANCED RESEARCH RESEARCH ARTICLE Cosmological models with Magnetized Anisotropic Dark Energy in Lyra Geometry V. R. Chirde, S. H. Shekh* Department of Mathematics, G. S. G. Mahavidyalaya, Umarkhed-445206.India Department of Mathematics, Dr. B.N.College of Engg.& Tech., Yavatmal-445001.India. Manuscript Info Abstract Manuscript History: Received: 12 April 2014 Final Accepted: 25 May 2014 Published Online: June 2014 Key words: Lyra Geometry, Dark Energy, Anisotropy. Corresponding Author Dr. Arathi Rao We have studiedanisotropic and homogenous Bianchi Type VI 0 space-time under the assumption of anisotropy of the fluid within the frame work of Lyra manifold in the presence and absence of magnetism. A special form of deceleration parameter which gives an early deceleration and late time accelerating cosmological models has been utilized to solve the field equations. The physical and geometrical behaviors of the model are also discussed. Copy Right, IJAR, 2014,. All rights reserved. INTRODUCTION One of the most intriguing modifications of general relativity is proposed by Weyl [1], invented to unify gravitation and electromagnetism by means of fundamental changes in Riemannian geometry. Unfortunately the Weyl theory suffers from non integrability of length which is physically unacceptable. However being interesting from mathematical point of view, it may still have the germs of a future fruitful theory. Later, Lyra [2] modified Riemannian geometry and removed non integrability of length transfer by introducing a gauge function into the structure-less manifold as a result of which a displacement field arises naturally. Subsequently, Sen et al. [3, 4] proposed a new scalar tensor theory of gravitation. They constructed an analog of the Einstein Field Equation based on Lyra’s geometry. Halford [5, 6] showed that the scalar -tensor treatment based on Lyra’s geometry predicts some effects within observational limitsas in Einstein’s theory. Several authors Sen and Vanstone [7], Bhamra [8], Karade and Borikar [9], Kalyanshetti and Wagmode [10], Reddy and Innaiah [11], Beesham [12], Reddy and Venkateswarlu [13], Soleng [14] had studied cosmological models based on Lyra’s manifold with a constant displacement field vector. However, this restriction of the displacement field to be constant is merely one for convenience and there is no priori reason for it. Beesham [15] have considered Friedmann-Robertson-Walker (FRW) models with time dependent displacement field. Singh et al. [16−[20] had studied Bianchi-type I, III, Kantowaski-Sachs and a new class of cosmological models with time dependent displacement field and have made a comparative study of Robertson-Walker models with constant deceleration parameter in Einstein’s theory with cosmological term in the cosmological theory based on Lyra’s geometry. Soleng [14] has pointed out that the cosmologies based on Lyra’s manifold with constant gauge vector φ will either include as creation field and be equal to Hoyle’s creation field cosmology [21−23] or contain a special vacuum field, which together with the gauge vector term may be considered as a cosmological term. Sri Ram and Singh [24] have obtained exact solutions of the field equations in vacuum and in the presence of stiff-matter for anisotropic Bianchi type V cosmological models in the normal gauge with a time- dependent displacement vector field. Singh [25] considered flat FRW mode l in Lyra’s geometry by using varying adiabatic equation of state and solved the field equations for the early phases of evolution of universe. Pradhan and Vishwakarma [26] have investigated a class of LRS Bianchi type I models in the cosmological theory based on Lyra’s geometry by considering a time-dependent displacement field for constant deceleration parameter of the