Hawking-Moss instanton in nonlinear massive gravity

TL;DR

This paper investigates Hawking-Moss instantons in nonlinear massive gravity, analyzing how tunneling rates depend on theory parameters and contrasting these findings with General Relativity.

Contribution

It introduces the study of vacuum tunneling via Hawking-Moss instantons within nonlinear massive gravity, highlighting parameter-dependent effects on tunneling rates.

Findings

Tunneling rate can be enhanced or suppressed compared to GR.

Constraints on the ratio of physical to fiducial Hubble parameters.

Potential form is constrained by the theory parameters.

Abstract

As a first step toward understanding a lanscape of vacua in a theory of non-linear massive gravity, we consider a landscape of a single scalar field and study tunneling between a pair of adjacent vacua. We study the Hawking-Moss (HM) instanton that sits at a local maximum of the potential, and evaluate the dependence of the tunneling rate on the parameters of the theory. It is found that provided with the same physical HM Hubble parameter $H_{HM}$, depending on the values of parameters $\alpha_3$ and $\alpha_4$ in the action, the corresponding tunneling rate can be either enhanced or suppressed when compared to the one in the context of General Relativity (GR). Furthermore, we find the constraint on the ratio of the physical Hubble parameter to the fiducial one, which constrains the form of potential. This result is in sharp contrast to GR where there is no bound on the minimum value of the potential.