A linearly Expanding Universe With Variable G and Lambda

Abstract

We have studied a cosmological model with a cosmological term of the form $\Lambda=3\alpha\fr{\dot R^2}{R^2}+\bt\fr{\ddot R}{R}+\fr{3\gamma}{R^2} \alpha, \ \bt \gamma$ are constants. The scale factor (R) is found to vary linearly with time for both radiation and matter dominated epochs. The cosmological constant is found to decrease as $t^{-2}$ and the rate of particle creation is smaller than the Steady State value. The model gives $\Omega^\Lambda=\fr{1}{3}$ and $\Omega^m=\fr{2}{3}$ in the present era, $\Omega^\Lambda=\Omega^m=\fr{1}{2}$ in the radiation era. The present age of the universe $(\rm t_p$) is found to be $\rm t_p=H_p^{-1}$ , where $\rm H_p$ is the Hubble constant. The model is free from the main problems of the Standard Model. Since the scale factor $\rm R\propto t$ during the entire evolution of the universe the ratio of the cosmological constant at the Planck and present time is $\rm\fr{\Lambda_{Pl}}{\Lambda_p}=10^{120}$. This decay law justifies why, today, the cosmological constant is exceedingly small.