Locally rotationally symmetric Bianchi type I massive string cosmological model with vacuum energy density and magnetic field in general relativity

A locally rotationally symmetric (LRS) Bianchi type I massive string cosmological model with vacuum energy density ([LAMBDA]) and magnetic field is investigated. To get a deterministic model of the universe, we assume that shear ([sigma]) is proportional to expansion ([theta]) and [LAMBDA] ~1/[R.sup.2] as considered by Chen and Wu (Phys. Rev. D, 41, 695 (1990)) where R is a scale factor. We find that the total energy density ([rho]), the particle density [[rho].sub.p] decreases with time. The strong energy conditions as given by Hawking and Ellis (The large scale structure of space-time. Cambridge University Press, Cambridge, UK. p. 88. (1974)) are satisfied. The vacuum energy density decreases with time, which matches with astronomical observation. The model in general represents anisotropic space-time because of the presence of strings. The total energy density and string tension density decrease because of the presence of a magnetic field. Both the models have point-type singularities at T = 0 and [tau] = 0, respectively. The other physical aspects of the models are also discussed. Key words: LRS, Bianchi I, massive string, cosmological, vacuum energy, magnetic field. Nous analysons un modele cosmologique de Bianchi de type I avec corde massive, localement symetrique sous rotation (LRS) et possedant une densite d'energie du vide ([LAMBDA]) et un champ magnetique. Afin d'obtenir un modele deterministe de l'univers, nous supposons que le cisaillement ([sigma]) est proportionnel a l'expansion ([theta]) et que [LAMBDA] ~ 1/[R.sup.2], tel que considere par Chen et Wu (Phys. Rev. D, 41, 695 (1990)) ou R est le facteur d'echelle. Nous trouvons que la densite totale d'energie ([rho]) et la densite de particules [[rho].sub.p] decroissent avec le temps. Les fortes conditions d'energie de Hawking et Ellis (The large scale structure of space-time. Cambridge University Press, Cambridge, UK. p. 88. (1974)) sont satisfaites. La densite d'energie du vide diminue avec le temps, ce qui correspond aux observations astronomiques. La presence de la corde fait que le modele represente un espace-temps anisotrope. La densite totale d'energie et la densite de tension de corde diminuent a cause du champ magnetique. Les deux modeles ont des singularites ponctuelles a T = 0 et [tau] = 0 respectivement. Nous discutons les autres aspects du modele. [Traduit par la Redaction] Mots-cles : localement symetrique sous rotation, Bianchi de type I, corde massive, cosmologique, energie du vide, champ magnetique. PACS Nos.: 04.50.Gh, 98.80.Cq, 98.80.-k.
1. Introduction The cosmological problem within the framework of general relativity is to find a model of the physical universe that correctly predicts the result of astronomical observation. The simplest [...]