If the Sterile Neutrino only feels Gravity (and not the Weak Force) how can it ever be detected? I assume current neutrino detectors would be useless.
By hypothesis, sterile neutrino would be difficult to detect directly (even by the standards of experimental neutrino physics) because we define them by their failure to participate in the only interaction that normal neutrino participate in (the weak interaction).
Accordingly we detect them by their effects on the physics of things we can access by direct experimental efforts.
The primary channel for observation of sterile neutrinos would be through high precision measurements of the mixing matrix of the three ordinary neutrino species, so that the unitarity of that matrix could be assessed with confidence.
Real quantum system are unitary, so if the (3-flavor) mixing matrix were found to be non-unitary to high confidence in some range of $L/E$, then we would infer the existence of some additional state (or states) of the system which none-the-less did not show up in our detectors. Because the detectors are (by design) sensitive to the kind of interaction that normal neutrino have, those state would necessarily not have that interaction channel.
Sterile Neutrinos are hypothetical they have not yet been proven to exist. We can't really detect them. There have been attempts to detect radiation given off by Sterile Neutrinos but with no success.
The production and decay of sterile neutrinos could happen through the mixing with virtual ("off mass shell") neutrinos. There were several experiments set up to discover or observe NHLs, for example the NuTeV (E815) experiment at Fermilab or LEP-l3 at CERN. They all led to establishing limits to observation, rather than actual observation of those particles. If they are indeed a constituent of dark matter, sensitive X-ray detectors would be needed to observe the radiation emitted by their decays
We have ideas of how we can detect them but we haven't actually ever detected one before.
A sterile neutrino was possible explanation of the results of the Liquid Scintillator Neutrino Detector experiment. Recent results and data have given support to the existence d of such a particle. Even though researchers at the MiniBooNE experiment at Fermilab announced that they had not found any evidence supporting the existence of such a sterile neutrino.
Two separate detectors near a nuclear reactor in France found 3% of anti-neutrinos missing. They suggested the existence of a 4th neutrino with a mass of 0.7 keV.
Daya Bay Collaboration measured the anti-neutrino energy spectrum, and found that anti-neutrinos at an energy of around 5 MeV are in excess relative to theoretical expectations. It also recorded 6% missing anti-neutrinos. This could suggest that Sterile neutrinos exist or that our understanding of Neutrinos is not complete.
The Seesaw mechanism As the sterile right-handed neutrino gets heavier, the normal left-handed neutrino gets lighter. The left-handed neutrino is a mixture of two Majorana neutrinos, and this mixing process is how sterile neutrino mass is generated.
Apart from empirical evidence, there is also a theoretical justification for the seesaw mechanism in various extensions to the Standard Model. Both Grand Unification Theories (GUTs) and left-right symmetrical models predict the following relation:
According to GUTs and left-right models, the right-handed neutrino is extremely heavy: MNHL ≈ 105—1012 GeV, while the smaller eigenvalue is approximately equal to