  Bimetric gravity theories describes gravitational interactions in the
presence of an extra spin-2 field. The Hassan-Rosen (HR) nonlinear massive
minimal bigravity theory is a ghost-free bimetric theory formulated with
respect a flat, dynamical reference metric. In this work the deformation
quantization formalism is applied to a HR cosmological model in the
minisuperspace. The quantization procedure is performed explicitly for quantum
cosmology in the minisuperspace. The Friedmann-Lema\^itre-Robertson-Walker
(FLRW) model with flat metrics is worked out and the computation of the Wigner
functions for theHartle-Hawking, Vilenkin and Linde wavefunctions are done
numerically and, in the Hartle-Hawking case, also analytically. From the
stability analysis in the quantum minisuper phase space it is found an
interpretation of the mass of graviton as an emergent cosmological constant and
as a measure of the deviation of classical behavior of the Wigner functions.
Also, from the Hartle-Hawking case, an interesting relation between the
curvature and the mass of graviton in a cusp catastrophe surface is discussed
