Vacuum decay and bubble nucleation in $f(R)$ gravity
  In this work we study vacuum decay and bubble nucleation in models of $f(R)$
higher curvature gravity. Building upon the analysis of Coleman-De Luccia
(CDL), we present the formalism to calculate the Euclidean action and the
bounce solution for a general $f(R)$ gravity in the thin wall approximation. We
calculate the size of the nucleated bubble and the decay exponent for the
Starobinsky model and its higher power extensions. We have shown that in the
Starobinsky model with a typical potential the nucleated bubble has a larger
size in comparison to the CDL bubble and with a lower tunneling rate. However,
for higher power extension of the Starobinsky model the size of the bubble and
the tunneling exponent can be larger or smaller than the CDL bubble depending
on the model parameters. As a counterintuitive example, we have shown that a
bubble with a larger size than the CDL bubble but with a higher nucleation rate
can be formed in $f(R)$ gravity.
