In this paper, we shall focus upon the problem of establishing a formalism for studying the massive string in Bianchi-III space-time in occurrence of magnetic field and bulk viscous fluid. The resource of the magnetic field is due to an electric current produced along the z-axis. F12 is the appearance component of electromagnetic field tensor. The Einstein’s equations can be solved in order to find which energy momentum tensor corresponds to a given geometry of space-time. This work presents the explicit expressions of the cosmological constant for the electromagnetic field and in the presence of bulk viscous fluid. The behaviour of the universe in this model will be determined by the cosmological Term. A positive value of ? corresponds to a negative effective mass density (repulsion). It is observed that the particle density and the tension density of the string are comparable at the two ends and they fall off asymptotically at similar rate. Some physical and geometric properties of the model are also discussed.

1. Itroduction.

Currently, cosmic strings have peaked considerable interest among the researchers for different features such as the study of the present Universe. Cosmic strings had appeared in the early Universe as topological faults as a result of a series of phase changes related to the natural breaking of internal symmetry 1, 2. The occurrence of cosmic strings in the currently Universe could be described using grand unified theories. These strings occur during the phase change after the Big Bang explosion as the temperature decrease under some critical point. It is supposed that the survival of strings in the currently Universe gives grow to the density variations which leads to the configuration of the galaxies 3–7. Moreover the cosmic strings have been used in attempts to study anisotropic dark energy component together with a mingling between dark energy and a perfect fluid (dark matter) 8, 9. The cosmic string is considered by a stress energy tensor and it is attached to the gravitational field.

The occurrence of magnetic fields in galactic and intergalactic spaces is well settled and their significance in as trophysics is generally recognized (see e.g. the reviews 10, 11 and references therein). In spite of the fact that the current magnitude of the magnetic energy is very small in association with the matter density, it might not have been minor during initial stages of the evolution of the Universe. Any cosmological model which holds magnetic fields is essentially anisotropic catching into account that the magnetic field vector implies a favoured spatial direction. The occurrence of primordial magnetic fields in the beginning stages of the evolution of the universe has been considered by several authors (Misner et al. 14; Asseo and Sol 15; Pudritz and Silk 16; Kim et al. 17; Perley and Taylor 18; Kronberg et al. 19; Wolfe et al. 20; Kulsrud et al. 21; Barrow 22). Melvin 23, in his cosmological solution for dust and electromagnetic field recommended that during the evolution of the universe, the matter was in a extremely ionized state and was efficiently attached with the field, consequently forming neutral matter as a result of universe inflation. Hence the occurrence of magnetic field in string dust universe is not idealistic. The string cosmological models with a magnetic field in Bianchi type I, II, III, V I0, VIII and IX space-times have been considered by several authors 24? 36. Currently, Pradhan et al. 37 considered Bianchi-I massive string cosmological models in general relativity. Currently, Yadav 38 and Yadav et al. 39 41 have considered Bianchi type-V, II and cylindrically symmetric inhomogeneous universe through a cloud of strings.

The cosmological constant ? in the situation of cosmology is a homogeneous energy density and to accelerate the expansion of the universe is caused by this energy. The relationship between matter density and expansion rate is changed due to introduction of a cosmological constant. Thus it would be recognized a matter dominated universe and in turn the growth of large scale structure of the universe is affected. The dynamics of the universe is described by the cosmological models with a cosmological constant. Evidence was found out and provided by the current observations of type Ia supernovae with the red shift upto about z ? 1 that we may be living in a low mass density universe being contributed by the non-relativistic matter to the total energy density of the universe of order of ?m ? 0.3 . In consequence major part of the matter contents remains unobserved in the universe. Hence it may assumed that there is some extra energy enough to attain the value total ?total = 1 expected by the inflationary theory. To give consistent physical interpretation of these observational facts proposal has been given to several physical models. It has been suggested by the observational and theoretical features that the most usual contestant for the absent energy is the vacuum energy density or the cosmological constant ? 30-31. On the other hand, the selected cosmological constant as a vacuum energy faces a severe fine tuning trouble, which claims that the value of ? must be 120 orders of magnitude more than its currently eyeballed value. The assumption of the possible explanation for a little ? term is that it is vigorously evolving and not constant. The universe develops from a former hotter and dense epoch, the valuable cosmological term also evolves and reduces to its present value 32-33.

When we study the Bianchi type models, we detect that the models include isotropic special cases and they allow arbitrarily small anisotropic levels at some minute of cosmic times. Bianchi type cosmological models are very important in the cognizance that these models are homogeneous and anisotropic, from which the development of isotropization of the universe is considered through the passage of time. Besides, from the theoretical point of view, anisotropic universe has a more than isotropic models. The plainness of the field equations made Bianchi space time helpful in constructing models of especially homogeneous and anisotropic cosmologies.

Motivated the situations discussed above, in this paper, we shall focus upon the problem of establishing a formalism for studying the massive string in Bianchi-III space-time in presence of magnetic field and bulk viscous fluid. Here we have obtained an exact and general solution of Einstein’s field equations of Bianchi type-III space-time for a cloud of strings with electromagnetic field. The paper is planned as follows. The metric and the field equations are existing in Section II. In Section III, we deal with an exact solution of the field equations with cloud of strings. In this section we also described three types of models of the universe. In Section IV we describe some physical and geometric properties of the model. Finally, in Section V, concluding remarks are given.