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 = βR̈/R where β is a constant. For an 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 H0-1, where H0 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 = 3αH2 (α = const) provided α = β/3(β-2). The inflationary solution obtained from this model is that of the de Sitter type.