The right-handed sterile neutrinos $\nu_{R}$ are electroweak singlets. They do not contribute to the electroweak anomaly, and therefore, their number is not fixed by the requirement of the anomaly cancellation. In particular, their number need not coincide with the number of generations $N$ but can be smaller or larger than $N$.

Question 1. Is there a bound on the number of sterile neutrinos from cosmological observations?

The cosmological bounds coming from the Planck and other experiments tells that the sum of the neutrino masses $\sum m_{\nu_i}$ is $<0.23~ {\rm eV }$ and the effective number of neutrinos is $N_{\rm eff}\approx 3$. I think these number $3$ counts the number of three active neutrinos because if it counts the total number of active+sterile species, there will be no scope for any sterile neutrino.

Question 2. Is there a separate bound on sterile neutrino number?

  • $\begingroup$ I remember that in one of my classes the professor told that the existence of only 1 sterile neutrino is heavily disfavored. However I don't remember the reason behind that. Maybe someone who got a good answer might also explain this... The effective number 3 is indeed only referring to active neutrinos. Regarding cosmological data: Despite very precise future oscillation data I cannot imagine any way to limit the number of sterile neutrinos because they only interact via mixing in the yukawa term. Very interesting question though. Would love to see if someone knows other possible methods $\endgroup$ Jan 18 '19 at 23:38

The SM prediction is fixed to be $N_\mathrm{eff} = 3.046$ (the 0.046 is due to decoupling effects and oscilations). So the important cosmological measurement is actually the deviation from this value, $\Delta N_\mathrm{eff}$. This can constrain New Physics models.

The measured bound directly applies to any relativistic (at the time of BBN) fermionic degree of freedom (DOF), including sterile neutrinos. And it indirectly applies also to bosonic DOF. These relativistic DOF are usually referred to as "dark radiation".

Current measurements show that $\Delta N_\mathrm{eff}$ is close to 0. In agreement with the SM and strongly disfavoring dark radiation.

  • $\begingroup$ A LaTeX quirk which is inherited by MathJax: consider using N_\mathit{eff} or N_\text{eff} to use the wordlike, rather than mathlike, kerning between the two fs in "effective." $\endgroup$
    – rob
    Jan 28 '19 at 14:36
  • $\begingroup$ I know this is a late response but can you please explain how $N_{\rm eff}$ is defined, what it really counts and how is it related to neutrinos? I could not follow the answer. @xi45 $\endgroup$
    – SRS
    Nov 18 '19 at 8:45

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