Cosmological consequences of a built-in cosmological constant model

Abstract

We have analyzed the implications of a phenomenological model of a built-in cosmological constant of Rastall and Al-Rawaf -Taha type. We have produced the presently observed cosmic acceleration with the aid of introducing a positive cosmological constant. We have shown that the cosmological models of the type $\Lambda \propto \frac{\ddot{R}}{R},\Lambda \propto H^2$ or $\Lambda \propto 8\pi G\rho$ are equivalent to a built-in cosmological constant model of Al-Rawaf and Taha type. Such models are compatible with the recent observational data and do not suffer from fine tuning problems. We predict a higher lensing probability than in Einstein de Sitter and Abdel Rahman models. We also predict a higher value for the luminosity and angular diameter distances than that of Abdel Rahman model. The lens distribution peaks at relatively smaller values of the lens red-shift and occurs at higher red-shift.

9 LaTex pages, 5 figures

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