Toward Quantum Gravity I: Newton Gravitation Constant, Cosmological Constant, and Classical Tests

TL;DR

This paper proposes a quantum gravity model using an SU(N) gauge theory with a  vacuum term, linking gauge boson properties to gravitational constants and explaining the small cosmological constant today.

Contribution

It introduces a novel SU(N) gauge theory framework for quantum gravity that relates gauge boson masses to gravitational and cosmological constants, explaining their observed values.

Findings

Realizes Newton's gravitational constant as an effective coupling of a massive graviton.

Provides a mechanism for the small current cosmological constant from gauge boson condensation.

Discusses relations among quantum gravity, general relativity, and Newtonian mechanics.

Abstract

This study toward quantum gravity (QG) introduces an SU(N) gauge theory with the \Theta vacuum term as a trial theory. Newton gravitation constant G_N is realized as the effective coupling constant for a massive graviton, G_N /\sqrt{2} = g_f g_g^2/8 M_G^2 \simeq 10^{-38} GeV^{-2} with the gauge boson mass M_G = M_{Pl} \simeq 10^{19} GeV, the gravitational coupling constant g_g, and the gravitational factor g_f. This scheme postulates the effective cosmological constant as the effective vacuum energy represented by massive gauge bosons, \Lambda_e = 8 \pi G_N M_G^4, and provides a plausible explanation for the small cosmological constant at the present epoch \Lambda_0 \simeq 10^{-84} GeV^2 and the large value at the Planck epoch \Lambda_{Pl} \simeq 10^{38} GeV^2; the condensation of the singlet gauge field <\phi> triggers the current anomaly and subtracts the gauge boson mass, M_G^2 = M_{Pl}^2 - g_f g_g^2 <\phi>^2 = g_f g_g^2 (A_{0}^2 - <\phi>^2), as the vacuum energy. Relations among QG, general relativity, and Newtonian mechanics are discussed.