  We study homogeneous gravitational instantons, conventionally called the
Hawking-Moss (HM) instantons, in bigravity theory. The HM instantons describe
the amplitude of quantum tunneling from a false vacuum to the true vacuum.
Corrections to General Relativity (GR) are found in a closed form. Using the
result, we discuss the following two issues: reduction to the de
Rham-Gabadadze-Tolley (dRGT) massive gravity and the possibility of preference
for a large $e$-folding number in the context of the Hartle-Hawking (HH)
no-boundary proposal. In particular, concerning the dRGT limit, it is found
that the tunneling through the so-called self-accelerating branch is
exponentially suppressed relative to the normal branch, and the probability
becomes zero in the dRGT limit. As far as HM instantons are concerned, this
could imply that the reduction from bigravity to the dRGT massive gravity is
ill-defined.
