How can right-handed neutrinos evade the SM experimental bound $N_\nu=3$ and become all the dark matter?
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The $N_{\nu}=3$ statement really is a statement about the number of species that the $Z$-Boson can decay into. That has been measured with amazing precision at LEP to be 3. You can prevent that, for example by making your new neutrino heavier than the $Z$, or by making it right-handed. Then that bound does not apply. You have invented a "sterile" neutrino that evades this bound.
Now, for that sterile neutrino I to be dark matter, you still have to satisfy the other constraints, e.g. from structure formation. In particular, you need to produce it in the early universe in such a way that it is "cold" (or "warm" at best), i.e., non-relativistic.
