  We investigate whether theories with two conjugate metrics g_{\mu \nu} and
$\tilde{g}_{\mu \nu} = \eta_{\mu \rho} \eta_{\nu \lambda} g^{\rho \lambda}$
where $\eta_{\mu \rho}$ is supposed to be a background non dynamical and flat
Minkowkian metric or an auxiliary field, actually predicted the occurrence of
apparently superluminal propagations (from our metric side $g_{\mu \nu}$ point
of view) such as the one recently reported by the Opera experiment. We find
that indeed such theories could predict the order of magnitude of the
superluminal velocity and even explain the apparent conflict with the SN1987
normal neutrino speeds provided the neutrinos are able to oscillate between the
two conjugate metrics while propagating in a dense medium. We then explain the
theoretical motivations and explore all possible phenomenological consequences
of the field discontinuities naturally expected in some Dark Gravity theories.
Since the Opera results was not confirmed, these discontinuities do not
actually allow a propagation of neutrinos oscillating between the two conjugate
metrics.
  Two attempted crosslists (gr-qc, hep-th) for this article were rejected
{\guillemotleft} upon a notice from Arxiv moderators, who determined the
submission to be inappropriate for the gr-qc (General Relativity and Quantum
Cosmology) and hep-th (High Energy Physics-Theory) subject classifications.
{\guillemotright}So if you think that this article and theoretical works in the
references deserve to be known by theorists (up to now, no other such kind of
predictions of supraluminous effects with the correct order of magnitude came
to my knowledge) please make it known.
