Time variation of the gravitational coupling constant in all dimensions: Kasner-type cosmological models

TL;DR

This paper investigates how the gravitational coupling constant varies over time across all dimensions, linking it to Newton's constant and extra dimensions, with specific analysis in Kasner-type cosmological models showing a decreasing trend in a 5D universe.

Contribution

It provides a model-independent formulation of the time variation of the gravitational coupling constant in all dimensions and applies it to Kasner-type cosmological models.

Findings

Gravitational coupling constant decreases over cosmic time in 5D models.

Rate of variation is approximately the inverse of the universe's age.

Results connect extra dimensions' volume change to gravitational constant variation.

Abstract

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.