Perfect fluid Bianchi Type-I cosmological models

with time varying G and L

J P SINGH^1,* and R K TIWARI²}

¹Department of Mathematical Sciences, A.P.S. University, Rewa 486 003, India

²Department of Mathematics, Govt. Model Science College, Rewa 486 001, India

^*Corresponding author

E-mail: jpsinghmp@lycos.com; rishitiwari59@rediffmail.com

Abstract. Bianchi Type-I cosmological models containing perfect fluid

with time varying $G$ and $\Lambda$ have been presented. The

solutions obtained represent an expansion scalar $\theta$ bearing a

constant ratio to the anisotropy in the direction of space-like unit

vector $\lambda^i$. Of the two models obtained, one has negative

vacuum energy density, which decays numerically. In this model, we

obtain $\Lambda \sim H^{2}$, $\Lambda \sim {R_{44}}/{R}$ and $\Lambda

\sim T^{-2}$ ($T$ is the cosmic time) which is in accordance with the

main dynamical laws for the decay of $\Lambda$. The second model

reduces to a static solution with repulsive gravity.

Keywords. Bianchi Type-I Universe; varying $G$ and $\Lambda$; cosmology.

PACS No. 98.80.Cq