Localized massive excitation of quantum gravity as a dark particle

Ken-Ji Hamada

doi:10.1103/physrevd.102.026024

Abstract

We construct a static and spherical excited state without singularities in renormalizable quantum gravity with background-free nature asymptotically. Its diameter is given by a correlation length of the quantum gravity, longer than the Planck length by 2 orders of magnitude, and it has a Schwarzschild tail outside. The quantum gravity dynamics inside is described by employing a nonperturbative expression of higher-order corrections assumed from a physical requirement that the dynamics disappear at the edge where it is in strong coupling. A running coupling constant that is a manifestation of nonlinearity and nonlocality is managed by approximating it as a mean field that depends on the radial coordinate. If the mass is several times the Planck mass, we can set up a system of linearized equations of motion for the gravitational potentials incorporating the running effect and obtain the excited state as its solution. It may be a candidate for dark matter, and will give a new perspective on black hole physics.

Highlights

In Einstein’s theory of gravity, a pointlike particle with mass beyond the Planck scale is a black hole
The dynamics of the asymptotically background-free quantum gravity begin to work at the energy scale ΛQG of 1017 GeV below the Planck scale
This means that before reaching the Planck scale, the spacetime enters a new phase dominated by the conformal dynamics of the quantum gravity

Summary

INTRODUCTION

In Einstein’s theory of gravity, a pointlike particle with mass beyond the Planck scale is a black hole. Describing the particle as a point is no longer justified This is the reason why the Planck scale has been recognized as a wall that cannot be exceeded. The quantities with the bar are the ones defined by gμν This action gives a kinetic term of the conformal factor field φ. Negative-metric modes are necessary components for the BRST conformal algebra to close at the quantum level, we can show that they all are not gauge invariant, and do not appear as physical states.. The theory has three physical scales, namely, renormalization group invariants [5] that must be determpiffinffiffiffied experimentally They are the Planck mass mpl 1⁄4 1= G ≃ 1019 GeV, the cosmological constant that is ignored here, and the dynamical scale ΛQG originated from the negativity of the beta function. The last one is the scale that separates quantum and classical spacetimes and is predicted to be ΛQG ≃ 1017 GeV from an inflation scenario driven by quantum gravity dynamics only [6,21,22,23]

EQUATIONS OF MOTION

SPHERICAL EXCITATIONS

ON TIME EVOLUTION

CONCLUSION AND DISCUSSION