LRS Bianchi Type II Massive String Cosmological Models with Magnetic Field in Lyra's Geometry

Bianchi type II massive string cosmological models with magnetic field and time dependent gauge function ( ) in the frame work of Lyra's geometry are investigated. The magnetic field is in -plane. To get the deterministic solution, we have assumed that the shear ( ) is proportional to the expansion ( ). This leads to , where and are metric potentials and is a constant. We find that the models start with a big bang at initial singularity and expansion decreases due to lapse of time. The anisotropy is maintained throughout but the model isotropizes when . The physical and geometrical aspects of the model in the presence and absence of magnetic field are also discussed. 1. Introduction Bianchi type II space time successfully explains the initial stage of evolution of universe. Asseo and Sol [1] have given the importance of Bianchi type II space time for the study of universe. The string theory is useful to describe an event at the early stage of evolution of universe in a lucid way. Cosmic strings play a significant role in the structure formation and evolution of universe. The presence of string in the early universe has been explained by Kibble [2], Vilenkin [3], and Zel’dovich [4] using grand unified theories. These strings have stress energy and are classified as massive and geometric strings. The pioneer work in the formation of energy momentum tensor for classical massive strings is due to Letelier [5] who explained that the massive strings are formed by geometric strings (Stachel [6]) with particle attached along its extension. Letelier [5] first used this idea in obtaining some cosmological solutions for massive string for Bianchi type I and Kantowski-Sachs space-times. Many authors’ namely, Banerjee et al. [7], Tikekar and Patel [8, 9], Wang [10], and Bali et al. [11–14], have investigated string cosmological models in different contexts. Einstein introduced general theory of relativity to describe gravitation in terms of geometry and it helped him to geometrize other physical fields. Motivated by the successful attempt of Einstein, Weyl [15] made one of the best attempts to generalize Riemannian geometry to unify gravitation and electromagnetism. Unfortunately Weyl’s theory was not accepted due to nonintegrability of length. Lyra [16] proposed a modification in Riemannian geometry by introducing gauge function into the structureless manifold. This modification removed the main obstacle of the Weyl theory [15]. Sen [17] formulated a new scalar tensor theory of gravitation and constructed an analogue of Einstein field equations based on Lyra