Feasibility of observing mechanical effects of cosmological neutrinos

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Abstract
We reexamine mechanical effects of cosmological neutrinos, and the possibility of their detection. Classical and quantum-mechanical results are derived for the mean force on a spherical target mass due to neutrinos that are either extremely relativistic, nonrelativistic but unclustered, or nonrelativistic and clustered; results are presented for Dirac and Majorana massive neutrinos. We find that there is no O(G(F)) mean force, in agreement with earlier calculations. In addition, we demonstrate that there are fluctuating forces O(G(F)(2)), which are more important than the mean force except on sufficiently long time scales that we evaluate case by case. Thus, fluctuations may act as a source of noise for any experiment seeking to detect the small, mean force due to background neutrinos even if all other sources of noise can be eliminated. In addition, we show that the fluctuating forces on a pair of nearby targets due to background neutrinos should be correlated, and that interference effects can lead to a short-range ''shadowing force'' between targets even in a perfectly isotropic background. Finally, the rates of phonon excitation both from the ground state and for a state with nonzero preexisting excitation are computed.