Varying Newton Gravitational “Constant” Cosmology

The Heisenberg uncertainty principle has significant implications for the vacuum state. It facilitates the spontaneous creation and annihilation of electron-positron pairs within the vacuum.

Consider a vacuum influenced by fluctuating gravitational fields. At a specific moment (T1), fluctuations in the gravitational constant (G) lead to the creation of an electron-positron pair at an initial energy level (E_initial) when G is at value G1. This pair subsequently falls a quantum wavelength to a lower energy level. Upon reaching this lower level, the gravitational constant has changed to G2, resulting in the spontaneous annihilation of the pair into gamma rays. These gamma rays then ascend back to the original energy level, where they generate a new electron-positron pair at event 3, with the gravitational constant now at G3.

During the transition from event 1 to event 2, the electron-positron pair experiences a change in gravitational potential energy, which should ideally be balanced by the gravitational Doppler shift of the gamma rays. This balance is only achieved if the gravitational constant remains constant across events 1, 2, and 3. In such a scenario, the initial and final energies of the electron-positron pair would be equal, resulting in no net radiation emission.

However, if G fluctuates—taking values G1 at event 1, G2 at event 2, and G3 at event 3—the initial and final energies of the electron-positron pair will differ, leading to an imbalance that prevents the gravitational Doppler shift from compensating. This variation in gravitational potential energy allows for the emission of Hawking radiation, indicating that all massive objects, not just black holes, can produce such radiation.

In contrast, Unruh radiation is not observable in relation to G fluctuations; it is instead associated with constant mechanical acceleration or with equivalent constant gravitational fields that do not involve fluctuations in G.