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That would imply a preferred direction in the universe (the axis of rotation) and thus anisotropy.
There are stringent constraints on anisotropy from the cosmic microwave background.
In particular, one can use the Doppler effect to check whether the CMB dipole is compatible with our velocity with respect to the CMB frame.
All these papers miss the fact that our main evidence for dark matter (or something like it) is the cosmic microwave background. I see no mention on how this very convoluted model can reproduce it.
The evidence is in the oscillations of the primordial plasma seen directly in the CMB. These come from the gravity pulling the plasma and pressure pushing back. Without DM they would be too shallow, DM helps by pulling the plasma gravitationally without opposing the fall with pressure of its own.
The computation of the cosmic microwave background fluctuations hasn't received a nobel prize yet. It's had a deep impact on how we understand the Universe.
Some people still alive who made important contributions to this are Rees and Sunyaev.