String cosmological models from early deceleration to current acceleration phase with varying G and $\Lambda$

Abstract.

Thepresent study deals with spatially homogeneous and anisotropic Bianchi-I cosmological models representing massive strings with variable G and decaying vacuum energy density $\Lambda$ . The energy-momentum tensor, as formulated by Letelier (Phys. Rev. D 20, 1294 (1979); Phys. Rev. D 28, 2414 (1983)), has been used to construct massive string cosmological models for which we assume the expansion scalar in the models is proportional to one of the components of shear tensor and barotropic EoS. The Einstein field equations have been solved by considering the time-dependent deceleration parameter which yields a scale factor $a(t) = (\sinh(\alpha t))^{\frac{1}{n}}$ , where n is a positive constant. For n > 1 , this generates a transition of the Universe from the early decelerating phase to the recent accelerating phase and the transition redshift z_t has been calculated. The study reveals that massive strings dominate the early Universe evolving with deceleration and in the later phase they disappear, which is in good agreement with current astronomical observations. The cosmological constant $\Lambda$ is found to be a positive decreasing function of time which is corroborated by results from recent Supernovae Ia observations. The physical and geometric properties of the models have been also discussed in detail.