Astrophys Space Sci (2011) 331: 697–704 DOI 10.1007/s10509-010-0478-8 ORIGINAL ARTICLE Anisotropic Bianchi type-I models in string cosmology Anirudh Pradhan · D.S. Chouhan Received: 13 August 2010 / Accepted: 1 September 2010 / Published online: 14 September 2010 © Springer Science+Business Media B.V. 2010 Abstract The present study deals with a spatially homoge- neous and anisotropic Bianchi-I cosmological models rep- resenting massive strings. The energy-momentum tensor, as formulated by Letelier (1983), has been used to construct massive string cosmological models for which we assume the expansion scalar in the models is proportional to one of the components of shear tensor. The Einstein’s field equa- tions have been solved by applying a variation law for gener- alized Hubble’s parameter in Bianchi-I space-time. We have analysed a comparative study of accelerating and decelerat- ing models in the presence of string scenario. The study re- veals that massive strings dominate in the decelerating uni- verse whereas strings dominate in the accelerating universe. The strings eventually disappear from the universe for suf- ficiently large times, which is in agreement with current as- tronomical observations. Keywords String · Bianchi-I universe · Accelerating universe 1 Introduction Since the observed universe is almost homogeneous and isotropic, space-time is usually described by a Friedman- Lemaitre-Robertson-Walker (FLRW) cosmology. But it is A. Pradhan ( ) Department of Mathematics, Hindu Post-Graduate College, Zamania, 232 331, Ghazipur, India e-mail: pradhan@iucaa.ernet.in D.S. Chouhan Department of Mathematics, School of Engineering, Sir Padampat Singhania University, Bhatewar, 313601, Udaipur, India e-mail: ds.chouhan@spsu.ac.in also believed that in the early universe the FLRW model does not give a correct matter description. The anomalies found in the cosmic microwave background (CMB) and the large structure observations stimulated a growing interest in anisotropic cosmological model of the universe. Observa- tions by the Differential Radiometers on NACA’s Cosmic Background Explorer registered anisotropy in various an- gle scales. It is conjectured, that these anisotropies hide in their hearts the entire history of the cosmic evolution down to recombination, and they are considered to be indicative of the universe geometry and the matter composing the uni- verse. It is expected, that much more will be known about anisotropy of cosmic microwave’s background after the in- vestigations of the microwave’s anisotropy probe. There is a general agreement among cosmologists that cosmic mi- crowave’s background anisotropy in the small angle scale holds the key to the formation of the discrete structure. The theoretical argument (Misner 1968) and the modern exper- imental data support the existence of an anisotropic phase, which turns into an isotropic one. In recent years, there has been considerable interest in string cosmology. Cosmic strings are topologically stable objects which might be found during a phase transition in the early universe (Kibble 1976). Cosmic strings play an im- portant role in the study of the early universe. These arise during the phase transition after the big bang explosion as the temperature goes down below some critical tempera- ture as predicted by grand unified theories (Zel’dovich et al. 1975; Kibble 1976, 1980; Everett 1981; Vilenkin 1981a). It is believed that the existence of strings in the early universe gives rise to the density fluctuations which leads to the for- mation of galaxies (Zel’dovich 1980; Vilenkin 1981b, 1985; Hindmarsh and Kibble 1995; Turner and Tyson 1999). Mas- sive closed loops of strings serve as seeds for the forma- tion of large structures like galaxies and cluster of galaxies.