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

TL;DR

The paper investigates a dynamical cut-off for quantum gravity, arguing that one-loop gravity–matter interactions generate a sub-Planckian scale Λ_E that is set by the unified gauge coupling via $\Lambda_E \sim \tilde m_{pl}\,\alpha_{gu}(\Lambda_E)/(4\pi)$, yielding $\Lambda_E \sim 10^{16}$ GeV for $\alpha_{gu}(\Lambda_E) \sim 1/25$. It supports this through a loop-induced kinetic term for the metric, a curvature–scale argument with $R$ and $\lambda_{gr}$, and a black-hole horizon consistency condition $1/r_E=\tilde\alpha\Lambda_E$ that together justify a sub-Planckian cut-off tied to grand unification. The analysis also discusses extensions to supersymmetric theories for gravitino dynamics and suggests a common origin for the inflationary plateau scale and gravity’s unification scale. Overall, the work links the gravitational cut-off to gauge coupling unification and the Planck mass, with potential implications for early Universe phenomenology and beyond-Standard-Model physics.

Abstract

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

Figures (2)

• Figure 1: One-loop contribution to the kinetic term of external source $\mathscr A_\mu$ coupled to the current $\bar{\psi}\,\gamma^\mu\psi$ with the charge $e$.
• Figure 2: One-loop contribution to the kinetic term of external source related with metric $g_{\mu\nu}$ and coupled to the current $T^{\mu\nu}$ with the charge $e^2_\textsc{gr}$.