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 (Λ) and magnetic field is investigated. To get a deterministic model of the universe, we assume that shear (σ) is proportional to expansion (θ) and Λ ∼ 1/R2 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 (ρ), the particle density ρp 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 τ = 0, respectively. The other physical aspects of the models are also discussed.