Spacetime Quantum Fluctuations, Minimal Length and Einstein Equations

TL;DR

This paper explores how quantum fluctuations of spacetime, characterized by a deformation parameter at Planck scales, modify Einstein's equations, highlighting significant effects at high energies.

Contribution

It introduces a deformation parameter to describe spacetime quantum fluctuations and shows how Einstein equations depend on this parameter at high energies.

Findings

Quantum fluctuations are described via a deformation parameter.

Einstein equations are modified to include the deformation parameter.

Effects are negligible at low energies but significant at Planck scales.

Abstract

In the process of work it has been found that space-time quantum fluctuations are naturally described in terms of the deformation parameter introduced on going from the well-known quantum mechanics to that at Planck scales and put forward in the previous works of the author. As shown, with the use of quite natural assumptions, these fluctuations must be allowed for in Einstein Equations to lead to the dependence of the latter on the above-mentioned parameter, that is insignificant and may be ignored at low energies but is of particular importance at high energies. Besides, some inferences form the obtained results are maid.