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I recently developed an idea that we can still preserve neutrino oscillations without neutrino mass.

The first thing to explain it the direct neutrino mass experiments. Review papers showed that the direct neutrino mass experiments only put upper limit not lower limit on it, arXiv:1307.0101. So I think this idea generally is corret.

I can also explain solar neutrino data. Since DM particles are more concentrated in the Sun, since solar neutrinos doesn't oscillate out of the Sun. And inside the sun we can still have all kinds of resonances such as we had before.

So the oscillation frequency depends linearly on the number density of the DM particles. More DM particles inside the Sun will give us smaller oscillation wavelength and also bring the MSW region closer to the solar core. However, as long as it is adiabatic MSW transition, we won't have any problem because we always go to the eigenstates of interactions with DM.

Using the Gramian matrix to test the linearized neutrino oscillations and test the controllability:

Ref

1. https://en.wikipedia.org/wiki/Controllability_Gramian