Accelerated Lyra's Cosmology Driven by Electromagnetic Field in Inhomogeneous Universe

Anirudh Pradhan,Padmini Yadav

doi:10.1155/2009/471938

Abstract

A new class of cylindrically symmetric inhomogeneous cosmological models for perfect fluid distribution with electromagnetic field is obtained in the context of Lyra's geometry. We have obtained solutions by considering the time dependent displacement field. The source of the magnetic field is due to an electric current produced along thez-axis. OnlyF12is a nonvanishing component of electromagnetic field tensor. To get the deterministic solution, it has been assumed that the expansionθin the model is proportional to the shearσ. It has been found that the solutions are consistent with the recent observations of type Ia supernovae, and the displacement vectorβ(t)affects entropy. Physical and geometric aspects of the models are also discussed in presence and absence of magnetic field.

Highlights

Introduction and MotivationsThe inhomogeneous cosmological models play a significant role in understanding some essential features of the universe such as the formation of galaxies during the early stages of evolution and process of homogenization
Senovilla 10 obtained a new class of exact solutions of Einstein’s equations without big bang singularity, representing a cylindrically symmetric, inhomogeneous cosmological model filled with perfect fluid which is smooth and regular everywhere satisfying energy and causality conditions
−8πTij, 2.8 where φi is the displacement field vector defined as φi 0, 0, 0, β t, 2.9 where other symbols have their usual meaning as in Riemannian geometry

Summary

Introduction and Motivations

The inhomogeneous cosmological models play a significant role in understanding some essential features of the universe such as the formation of galaxies during the early stages of evolution and process of homogenization. 58 , Soleng 59 , have studied cosmological models based on Lyra’s manifold with a constant displacement field vector. Soleng 59 has pointed out that the cosmologies based on Lyra’s manifold with constant gauge vector φ will either include a creation field and be equal to Hoyle’s creation field cosmology 66–68 or contain a special vacuum field, which together with the gauge vector term, may be considered as a cosmological term In the latter case the solutions are equal to the general relativistic cosmologies with a cosmological term. Rahaman 84–87 has studied some topological defects within the framework of Lyra geometry With these motivations, in this paper, we have obtained exact solutions of Einstein’s modified field equations in cylindrically symmetric inhomogeneous space-time within the frame work of.

The Metric and Field Equations

Solution of Field Equations in Presence of Magnetic Field

C bα 1

Field Equations and Their Solution in Absence of Magnetic Field

Discussion and Concluding

B4 C4 ABC ββ4