Hawking-Moss instanton in nonlinear massive gravity
  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.
