Vacua in novel 4D Einstein-Gauss-Bonnet gravity: Pathology and instability?

Fu-Wen Shu

doi:10.1016/j.physletb.2020.135907

Abstract

We show an inconsistence of the novel 4D Einstein-Gauss-Bonnet gravity by considering a quantum tunneling process of vacua. Based on standard semiclassical techniques, we find a nonperturbative way to the study of the vacuum decay rate of the theory. We analytically compute all allowed cases in the parameter space. It turns out, without exception, that the theory either encounters a disastrous divergence of vacuum decay rate, or exhibits a confusing complex value of vacuum decay rate, or involves an instability (a large vacuum mixing). These suggest a strong possibility that the theory, at least the vacuum of the theory, is either unphysical or unstable, or has no well-defined limit as D→4.

Highlights

It was recognized a long time ago that the GaussBonnet term in four dimensions is a topological surface term and has no contribution to the dynamical degrees of freedom of the equations of motion
By rescaling the coupling constant α of the Gauss-Bonnet term to α/(D − 4), and defining the four-dimensional theory as the limit D → 4, the authors of [3] propose a novel theory of gravity in 4-dimensional spacetime where the Gauss-Bonnet term gives rise to nontrivial dynamics and the theory respects Lovelocks theorem
Our results show that the theory either suffers a divergent vacuum decay rate, or possesses a puzzling complex value of the decay rate, or appears a large vacuum mixing

Summary

INTRODUCTION

It was recognized a long time ago that the GaussBonnet term in four dimensions is a topological surface term and has no contribution to the dynamical degrees of freedom of the equations of motion. Our efforts are divided in two folds: Classically, we find that the pure vacuum itself is free of the subtlety found in [29], and is stable at the classical level though it has a ghost coupling for the Gauss-Bonnet vacuum. Once it couples with matter, non-spherically symmetric solutions can excite a freely propagating tensor mode [34]. All these strongly indicate that the theory, at least the vacuum of the theory, is either unphysical or unstable, or has no well-defined limit as D → 4

VACUA OF THE THEORY

VACUUM DECAY OF THE THEORY

Bubble geometry

Bubble nucleation

SUMMARY