On Robertson-Walker universe model with variable cosmological term and gravitational constant in cosmological relativity theory

This paper presents cosmological models in which the gravitational and cosmological constants G and Λ are time-dependent. We find a variety of solutions for the variation of cosmological parameters. It is also found that, in the case of matter dominated Robertson-Walker Universe, if the cosmological constant Λ ≠ 0, the Hubble’s constant H is not constant at all but inversely proportional to the cosmic time. The conservation law for the energy momentum tensor is still valid with our law of variation: Λ ∝ R^−2 and Gρ ∝ Λ/8π.