Varying Newton gravitational “constant” cosmology

We demonstrate that quantum random fluctuations of Newton’s “constant”, $G$, are required to allow the vacuum to radiate Hawking radiation when it is disturbed by a mass, whether it be a black hole or not. We deduce, from Heisenberg uncertainty principle, the maximum quantum fluctuation amplitude of an energy-dependent Newton gravitational “Constant” $G$. This allows us to deduce a cosmic law for the variation of $G$ as a function of the cosmological redshift. Consequences for the Friedman–Lemaître–Robertson–Walker (FLRW) Model of the Universe are explored and the physical nature of the Dark Matter (DM) components of the cosmological fluid is revealed. It is also argued that oscillations of $G$ in black holes are a new physical mechanism for the emission of Gravitational Waves (GWs). Thus, conversion of part of the black hole rest mass into GW energy, through this mechanism, should occur in all black holes present in Active Galactic Nuclei (AGN) accounting for their luminosity and for the Stochastic Gravitational Wave Background (SGWB) recently detected by Timing Pulsar Array (TPA) teams. The presented data analysis obtains the result that fluctuations of Newton “constant” $G$ allow for explaining several Cosmology experimental results, such as: Hubble Tension, DM density, and fire wall paradox.