Quantum Gravity in Plebanski Formulation

TL;DR

This paper proposes a nonperturbative four-dimensional quantum gravity theory in Plebanski formulation, predicting tiny graviton masses and a very small coupling constant, suggesting potential renormalizability.

Contribution

It introduces a novel nonperturbative quantum gravity model with massive gravitons in Plebanski formulation, exploring renormalizability and tiny graviton masses.

Findings

Predicted graviton mass ~ 1.8×10^{-42} GeV

Coupling constant ~ 10^{-61}

Supports idea of multi-graviton renormalizable quantum gravity

Abstract

We present a theory of four-dimensional quantum gravity with massive gravitons which may be essentially renormalizable. In the Plebanski formulation of General Relativity (GR), in which the tetrads, the connection and the curvature are all independent variables (and the usual relations among these quantities are valid only on-shell), we consider a nonperturbative theory of gravity with a nonzero background connection. We predict a tiny value of the graviton mass: m_g\approx 1.8\times 10^{-42} GeV and an extremely small dimensionless coupling constant of the perturbative gravitational interaction: g ~ 10^{-61}. We put forward the idea by H. Isimori on renormalizability of quantum gravity having multi-gravitons with masses m_0, m_1,..., m_{N-1}.