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We suggest a law for the decay of the effective cosmological constant of the form [Formula: see text]. It is shown that this provides more room for consistency with the recent observational data on Hubble's constant and the age of the universe.

We show that a previously proposed cosmological model based on general relativity with non vanishing divergence for the energy-momentum tensor is consistent with the observed values for the nucleosynthesis of helium for some values of the arbitrary parameter α presented in this model. Further more values of α can be accommodated if we adopt the Randall-Sundrum single brane model.

In this paper we propose a specific modification for Friedmann equation which leads during the matter-dominated era to a Cardassian type model, with the usual two undetermined parameters but with an important difference however, the usual parameter B which is constant in the Cardassian model becomes a function of time in this model. We found that although the model leads to acceleration at recent epoch. The acceleration values are more moderate than in the usual Cardassian model because B(t) is a reducing function of time. The model further leads to an increase in the abundance of light element during nucleosynthesis. We use the difference between the predicted and measured values of big bang nucleosynthesis of helium to obtain a value for n and B(t).