Cut-off scale of quantum gravity as a sign to unify interactions

TL;DR

This paper proposes that the cut-off scale of quantum gravity, derived from one-loop effective field theory, naturally aligns with the grand unification scale around 10^{16} GeV, linking gravity and gauge interactions.

Contribution

It introduces a relation connecting the quantum gravity cut-off scale with gauge coupling and Planck mass, suggesting a natural unification point.

Findings

The cut-off scale is estimated to be around 10^{16} GeV.

The derived scale aligns with the inflationary cosmology scale.

The relation incorporates gauge coupling constants into quantum gravity scale estimation.

Abstract

Dynamics of gravity interaction with matter at one-loop level of effective quantum field theory naturally sets the cut-off scale $\Lambda_E$ in a sub-Planckian region through incorporating the gauge coupling constant $\alpha(\Lambda_E)$ and the reduced Planckian mass $\tilde m_\text{pl}$ into relation $ \Lambda_E\sim \tilde m_\text{pl}\,\alpha(\Lambda_E)/(4\pi)$ numerically yielding $\Lambda_E\sim 10^{16}$ GeV. Such two scales are empirically inherent for an inflationary cosmology.