Varying Newton Gravitational “Constant” Cosmology

The oscillations of the event horizon in Schwarzschild black holes, caused by fluctuations in the gravitational constant (G), introduce a novel mechanism for the emission of gravitational waves. We assume that the amplitudes of these gravitational waves correspond to those detected by various Pulsar timing array teams, which have been associated with the Stochastic Gravitational Wave Background.

Our analysis reveals a linear relationship between the mass of black holes and redshift, illustrated in green on the graph. The continuous red line represents the linear fit of the experimentally observed masses of different black holes across varying redshifts, which aligns closely with the theoretical predictions depicted by the continuous green line, falling within the standard error of the mean.

Furthermore, the variation of G in Einstein's field equations necessitates a re-evaluation of the Friedmann-Lemaître-Robertson-Walker cosmological equation concerning the universe's matter and energy content. Our findings suggest that fluctuations in Newton's gravitational constant can account for approximately 24.24% of dark matter, with the remaining 2.16% attributable to torsion, as shown in the equation in the lower left corner of the slide. In this equation, δG represents the matter density resulting from variations in G, while ρₜ denotes the matter density due to torsion.

Additionally, the varying G concept addresses the Hubble tension by suggesting that G fluctuations were more pronounced during the Cosmic Microwave Background (CMB) epoch compared to the Cepheid period. Our approach also resolves the firewall paradox, demonstrating that an observer at rest on a black hole's event horizon perceives the same radiation as an observer in free fall through the horizon. This observation indicates that the radiation is solely dependent on the amplitude of gravitational field fluctuations at the horizon.