Talking about dark matter:
Now that SUSY hypothesis finally seems wrong, could be mathematically consistent to postulate that dark matter maybe a field whose particles don't interact at all with our "ordinary" matter (nor by the electroweak force neither by strong nuclear force) and that just by deforming the space-time with its mass(in a GR way) it disturbs indirectly the "ordinary" matter?
In other words, there could exists (transparents) fields unable to couple (in any way) to the known (accessible) ones? there could exists something like a separate set of fields forming a "dark" lagrangian ("dark" to us in the sense this L does not interact with our SM one) and that then this independient set of "dark" fields could be phenomenology presented to us only by the deformation their mass produce in the space-time?
Moreover, could an explanation of this type be behind also of dark energy in some way (maybe the equivalent of a "dark Higgs" mechanism with a special & different breaking potential)?
In summary: in contrast to the WIMPs hypothesis that talks about "interactions only through the weak nuclear force and gravity, or possibly other interactions with cross-sections no higher than the weak scale ", I refer to an hypothetical set of new fields that only interacts (with "ordinary" matter) indirectly though gravity in a general relativity manner (and nothing else). In fact, these fields would have their own lagrangian with no relation at all with the SM one (in low energy scales, possible unifying at very high energies).
And just to make it clear, I don't talk about the sterile neutrino hypothesis (a "simple" extension of the current standard model) because: "[sterile neutrino would] have Yukawa interactions with ordinary leptons and Higgs bosons, which via the Higgs mechanism lead to mixing with ordinary neutrinos". I.e.; they'd still could interact with (decay into) "ordinary" matter (they are WIMPs after all and I don't refer to that). By contrast, I'd like to know about the possibility of a fully non interacting massive particles as dark matter candidate. As I said we'd be a fully independent set of fields unable to interact at all with the SM particles except but the gravity generated by their mass in a GR way (just disturbing the space-time).
So, what do you think? There could exist two set of fields each one with its own lagrangian conforming a particular (and totally unrelated) gauge interaction model: something like an "ordinary" particle model ("light" standard model) and a independent -and unknown- "dark" particle model ("dark" standar model). We'd have also the classic general relativity that would feel the mass effects of the particles of the two set of fields and that'd be the responsible of the gravity interaction we observe between the "ordinary" matter and the "dark" matter. This hypothesis would be consistent at low energy scales but it could unify at very high energies where the quantum gravity would replace the classic general relativity approximation.
