  The recent direct detection of gravitational waves has highlighted the huge
importance of the tensorial modes in any extended gravitational theory. One of
the most appealing approaches to extend gravity beyond general relativity is
the Eddington-inspired-Born-Infeld gravity which is formulated within the
Palatini approach. This theory can avoid the Big Bang singularity in the
physical metric although a Big Bang intrinsic to the affine connection is still
there, which in addition couples to the tensorial sector and might jeopardize
the viability of the model. In this paper, we suggest that a quantum treatment
of the affine connection, or equivalently of its compatible metric, is able to
rescue the model. We carry out such an analysis and conclude that from a
quantum point of view such a Big Bang is unharmful. We expect therefore that
the induced tensorial instability, caused by the Big Bang intrinsic to the
affine connection, can be neutralized at the quantum level.
