ar X iv : g r - qc / 9 90 60 45 v 2 1 5 Ju n 19 99 FRW - TYPE UNIVERSE WITH VARIABLE G AND Λ Arbab

We have considered a cosmological model with a cosmological term of the form Λ = 3α ˙ R 2 R 2 + β ¨ R R , α, β = cont. The cosmological term is found to decrease as t −2 and the rate of particle creation is smaller than the Steady State value. Solutions with β = 3α in the radiation dominated era and β = 6α in the matter dominated era are equivalent to the FRW results. We have found an inflationary solution of the de-Sitter type with β = 3 − 3α. The model is found to resolve the problems of the Standard Model. Very recent results [1] suggest that the age of the universe is about 11 − 14 billion years. However results obtained from Standard Model of cosmology are not consistent with these findings. Numerous models have been presented to reconcile these contradiction with observations. Only few of these models have given a satisfactory solution. The presence of a cosmological constant (Λ) in a given cosmology prolongs the age of the universe. The inflationary paradigm requires the Universe to have a critical density but observations do not support this. One of the motivations for introducing Λ term is to reconcile the age parameter and the density parameter of the universe with current observational data. In an attempt to resolve these problems with current observations, we suggest a variation law for the cosmological constant of the form Λ = 3α ˙ R 2 R 2 + β ¨ R R , α, β = const. Observational data indicate that Λ ∼ 10 −55 cm −2 while particle physics prediction for Λ is greater than this value by a factor of order 10 120. This discrepancy is known as the cosmological constant problem. It is interesting that this decay law helps to resolve this problem. The entropy problem which exists in the Standard Model can be solved by the proposed decay law. The success of the inflationary model in extending the Big Bang model strengthen the theoretical prejudice toward a flat universe. In this paper we will consider a flat universe. Therefore this model preserves the spirit of the inflationary scenario. This inflationary solution is built in the model. The present model resolves many, if not all, of Standard Model