  It is known that the no-boundary proposal in the traditional Einstein gravity
does not prefer inflation, that is, the probability of realizing a large number
of e-folds is exponentially suppressed. This situation may be changed
drastically in a class of nonlinear massive gravity theories recently proposed
by deRham, Gabadadze and Tolley, called dRGT massive gravity. We show that the
contribution from the massive gravity sector can enhance the probability of a
large number of e-folds substantially for a sufficiently large mass parameter
mg comparable to the Hubble parameter during inflation, say $m_g \gtrsim
10^{12}$ GeV. We illustrate possible models to trigger such a large mass
parameter in the early universe while it is negligibly small in the present
universe. This opens a new window to explore the inflationary scenario in the
context of quantum cosmology.
