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

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.

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