Commun. Theor. Phys. (Beijing, China) 54 (2010) pp. 950–956 c  Chinese Physical Society and IOP Publishing Ltd Vol. 54, No. 5, November 15, 2010 Massive String Cosmology in Bianchi Type III Space-Time with Electromagnetic Field Anirudh Pradhan, 1,* Suman Lata, 1 and H. Amirhashchi 2,† 1 Department of Mathematics, Hindu Post-graduate College, Zamania-232 331, Ghazipur, India 2 Department of Physics, Mahshahr Islamic Azad University, Mahshahr, Iran (Received June 28, 2010; revised manuscript received August 12, 2010) Abstract Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (1983) in presence of perfect fluid and electromagnetic field. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value σ 2 2 of the shear tensor σ j i and also the fluid obeys the barotropic equation of state. It is observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. It is also observed that the string phase of the universe disappears in our model because particle density becomes negative. Some physical and geometric properties of the model are also discussed. PACS numbers: 98.80.Cq, 04.20.-q, 04.20.Jb Key words: massive string, exact solution, perfect fluid, electromagnetic field 1 Introduction One of the outstanding problems in cosmology today is developing a more precise understanding of structure formation in the universe, that is, the origin of galaxies and other large-scale structures. Existing theories for the structure formation of the universe fall into two categories, based either upon the amplification of quantum fluctua- tions in a scalar field during inflation, or upon symme- try breaking phase transition in the early universe, which leads to the formation of topological defects such as do- main walls, cosmic strings, monopoles, textures and other “hybrid” creatures. Cosmic strings play an important role in the study of the early universe. Cosmic strings are topologically stable objects, which might be found during a phase transition in the early universe. [1] These arise dur- ing the phase transition after the big bang explosion as the temperature goes down below some critical temperature as predicted by grand unified theories. [1-6] It is believed that the existence of strings in the early universe gives rise to the density fluctuations, which leads to the forma- tion of the galaxies. [7-11] Massive closed loops of strings serve as seeds for the formation of large structures like galaxies and cluster of galaxies. While matter is accreted onto loops, they oscillate violently and lose their energy by gravitational radiation and therefore they shrink and disappear. The general relativistic treatment of strings was ini- tiated by Letelier, [12-13] and Stachel. [14] Letelier [12] has obtained the solution to Einsteins field equations for a cloud of strings with spherical, plane and cylindrical sym- metry. Then, in 1983, he solved Einsteins field equations for a cloud of massive strings and obtained cosmological models in Bianchi I and Kantowski–Sachs space-times. Benerjee et al. [15] have investigated an axially symmet- ric Bianchi type I string dust cosmological model in pres- ence and absence of magnetic field. The string cosmo- logical models with a magnetic field are also discussed by Chakraborty. [16] Tikekar and Patel [17] have discussed some Bianchi type VI 0 string models with and without magnetic fields. Tikekar and Patel, [18] following the tech- niques used by Letelier and Stachel, obtained some ex- act Bianchi III cosmological solutions of massive strings in presence of magnetic field and also with vanishing magnetic field. Maharaj et al. [19] investigated the inte- grability of cosmic string in Bianchi type III space-time using a symmetry analysis and generalized the previous solutions obtained by Tikekar and Patel. [18] Patel and Maharaj [20] investigated stationary rotating world model with magnetic field. Ram and Singh [21] obtained some new exact solutions of string cosmology with and with- out a source free magnetic field for Bianchi type I space- time in the different basic form considered by Carmi- nati and McIntosh. [22] Exact solutions of string cosmol- ogy for Bianchi type II, VI 0 , VIII and IX space-times have been studied by Krori et al. [23] and Wang. [24] Singh and Singh [25] investigated string cosmological models with magnetic field in the context of space-time with G 3 sym- metry. Singh [26] has also studied string cosmological mod- els with electromagnetic field in Bianchi type II, VIII, and IX space-times. Singh [27] also obtained static mod- els of cosmic strings in general relativity. Lidsey, Wands, and Copeland [28] have reviewed aspects of super string cosmology with the emphasis on the cosmological impli- cations of duality symmetries in the theory. Recently Yadav et al. [29] have studied some Bianchi type I vis- cous fluid string cosmological models with magnetic field. * E-mail: acpradhan@yahoo.com † E-mail: hashchi@yahoo.com