Varying Newton Gravitational “Constant” Cosmology

Newton assumed that the gravitational constant, G, was constant in his law of universal gravitation primarily because he viewed space and time as absolute. This perspective allowed for the possibility of defining a universal present moment, suggesting that the speed of gravitation, like other interactions in Newtonian mechanics, could be infinite. Consequently, gravitation could always escape its own pull, meaning there was no gravitational cutoff length. This notion implies that black holes cannot exist within the framework of classical mechanics.

In contrast, Einstein's theory of relativity introduces a four-dimensional geometric continuum known as the space-time continuum. In this framework, gravitational interactions propagate at a finite speed—the speed of light. This leads to the existence of a gravitational cutoff length, specifically the Schwarzschild radius, thereby making black holes feasible within relativistic mechanics.

If G remains constant, black holes would be unable to interact gravitationally with the universe, as their gravitational pull would not allow for escape. However, if G fluctuates, gravitation could escape from black holes when the value of G permits escape speeds that are less than the speed of light. In this scenario, black holes could interact with the universe, potentially behaving as scintillating objects that emit flashes of light and gravitational waves.

To account for a varying gravitational constant, we propose a relationship between quantum gravity and the gravitational cutoff length of a system, equating the quantum length that characterizes a quantum system with this cutoff length.