  We consider a cosmological model in which the tensor mode becomes massive
during inflation, and study the Cosmic Microwave Background (CMB) temperature
and polarization bispectra arising from the mixing between the scalar mode and
the massive tensor mode during inflation. The model assumes the existence of a
preferred spatial frame during inflation. The local Lorentz invariance is
already broken in cosmology due to the existence of a preferred rest frame. The
existence of a preferred spatial frame further breaks the remaining local SO(3)
invariance and in particular gives rise to a mass in the tensor mode. At linear
perturbation level, we minimize our model so that the vector mode remains
non-dynamical, while the scalar mode is the same as the one in single-field
slow-roll inflation. At non-linear perturbation level, this inflationary
massive graviton phase leads to a sizeable scalar-scalar-tensor coupling, much
greater than the scalar-scalar-scalar one, as opposed to the conventional case.
This scalar-scalar-tensor interaction imprints a scale dependent feature in the
CMB temperature and polarization bispectra. Very intriguingly, we find a
surprizing similarity between the predicted scale dependence and the
scale-dependent non-Gaussianities at low multipoles hinted in the WMAP and
Planck results.
