Cosmological Transition of LRS Universe Model in Saez-Ballester Theory of Gravitation with Time Varying $G$ and $\Lambda$

Résumé

The presence of cosmic strings and dissipative effects with time varying gravitational constant $G$ and cosmological constant $\Lambda$, during the evolution of Universe, have been investigated by taking spatially homogeneous and locally rotationally symmetric (LRS) Bianchi type-II space-time. Moreover, by considering suitable physical assumptions, cosmological solutions to Einstein's field equations have been found out and their kinematical behaviour have been analysed in a theory proposed by Saez and Ballester (Phys. Lett. A 113: 467, 1986). Further, it has been noticed that $\Lambda$ is positive (but small) and of decreasing nature in scalar-tensor theory of gravitation but it shows an exact reverse behaviour in general theory of relativity for the entire evolution of Universe.