Time variation of the gravitational coupling constant in all dimensions:   Kasner-type cosmological models
  We formulate the time variation of the gravitational coupling constant in all dimensions. We show that the time variation of the gravitational coupling constant is related to the time variation of the Newton's constant in three-space dimensions and also is related to the time variation of the volume of the extra spatial dimensions. Our results here are based on a model-independent approach. We then study time variation of the gravitational coupling constant in Kasner-type cosmological models. In the case of $(4+1)$-dimensional spacetime we show that the gravitational coupling constant decreases within the cosmic time and the rate of its time variabilty is of the order of the inverse of the present value of the age of the universe. 
Forough Nasseri