Formulating and indirectly proving the quantum fluctuations of space-time and a justification for applying fractional quantum gravity

TL;DR

This paper formulates a mathematical model of quantum gravity with fractional equations, indirectly proves quantum fluctuations of space-time, and links fractional gravity to stochastic quantum fluctuations, explaining its empirical success.

Contribution

It introduces a fractional formulation of quantum gravity and provides a logical basis for fractional gravity as arising from quantum fluctuations of space-time.

Findings

Quantum fluctuations induce fractional gravity.

Transition from decelerated to accelerated expansion observed.

Fractional gravity linked to stochastic quantum fluctuations.

Abstract

It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old theory of quantum gravity, the result of which is that the equations of quantum gravity become fractional. The existence of such fluctuations is proved indirectly. On the other hand, recent attention has been paid to fractional gravity. Although this type of gravity leads to brilliant results, we have no root and logical reason for applying it other than that it works. We actually simultaneously demonstrate that fractional gravity is generated by stochastic quantum fluctuations of space-time. For clarification, Einstein-Hilbert theory along with a scalar field is investigated in deformed and non-deformed minisuperspaces. The results illustrate a transition from decelerated to accelerated expansion (late-time-accelerated expansion).