Varying Newton Gravitational “Constant” Cosmology

Dr.-Ing. Clovis Jacinto de Matos

Slide at 03:42

Heisenberg uncertainty cause G fluctuations
Quantum laws for gravitation appear when the size of a quantum system equals a gravitational cutoff scale l, which varies in
function of the Quantum gravity theory one adopts:
In string theory it is the string length In loop quantum gravity it is the diameter of the loop
In Physics Cell quantum gravity, it is the physics cell diameter
Compton length = Gravitational cutoff length
Independently of the quantum gravity theory adopted, Newton's constant depends on a cutoff length scale (energy scale)
Variations of the cutoff length Al will cause variations AG of G
Applying Heisenberg uncertainty principle to the cutoff length scale
Yields (assuming a Gaussian distribution centred on the Newtonian value GN):

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Summary (AI generated)

In various theories of quantum gravity, the concept of the gravitational cutoff length differs significantly. In string theory, it is defined as the size of the string. In loop quantum gravity, it corresponds to the diameter of the loop. Additionally, in the recently developed PC approach to quantum gravity, proposed by my co-author Nicolas Lori, the gravitational cutoff length is linked to the diameter of what we refer to as the physics cell, abbreviated as PC.

Regardless of the quantum gravity theory employed, it is consistently observed that Newton's gravitational constant, G, is influenced by the gravitational cutoff length scale. Variations in this scale can lead to fluctuations in the value of G. By applying the Heisenberg uncertainty principle to the gravitational length scale, we find that the relative fluctuation of G is constrained to be less than or equal to 1/2π.