  We discuss the detectability of gravitational waves with a time dependent
mass contribution, by means of the stochastic gravitational wave observations.
Such a mass term typically arises in the cosmological solutions of massive
gravity theories. We conduct the analysis based on a general quadratic action,
and thus the results apply universally to any massive gravity theories in which
modification of general relativity appears primarily in the tensor modes. The
primary manifestation of the modification in the gravitational wave spectrum is
a sharp peak. The position and height of the peak carry information on the
present value of the mass term, as well as the duration of the inflationary
stage. We also discuss the detectability of such a gravitational wave signal
using the future-planned gravitational wave observatories.
