Cosmic Acceleration With A Positive Cosmological Constant

Abstract

We have considered a cosmological model with a phenomenological model for the cosmological constant of the form $Λ=\bt\fr{\ddot R}{R}$, $ \bt$ is a constant. For age parameter consistent with observational data the Universe must be accelerating in the presence of a positive cosmological constant. The minimum age of the Universe is $H_0^{-1}$, where $H_0$ is the present Hubble constant. The cosmological constant is found to decrease as $t^{-2}$. Allowing the gravitational constant to change with time leads to an ever increasing gravitational constant at the present epoch. In the presence of a viscous fluid this decay law for $Λ$ is equivalent to the one with $Λ=3αH^2$ ($α=\rm const.$) provided $α=\fr{\bt}{3(\bt-2)}$. The inflationary solution obtained from this model is that of the de-Sitter type.