Long Range Forces from the Cosmological Neutrino Background

The cosmological neutrino background will mediate long range forces between objects. For a background of temperature T, the potential decreases as 1/r 5 for r >> 1/T and as 1/r for r << 1/T. These forces have large spin-dependent components. If the neutrino background is nonrelativistic, the long range forces are enhanced by a factor of the inverse neutrino velocity. These long range forces may provide a method for observing the cosmological neutrino background. 1 Ever since the neutrino was suggested by Pauli, there have been speculations about the long range forces produced by neutrino exchange ([1, 2] and references therein). Feinberg and Sucher found a potential which falls off like 1/r 5 with distance from two neutrino exchange in vacuum. Exchange of an even number of neutrinos is required in vacuum in order to leave the spin of the external particles unchanged, so that the effects of the potential can sum coherently over many particles. However in a background of neutrinos, single neutrino exchange can mediate a coherent, long range force because the background can supply and absorb one of the neutrinos. This is a realistic possibility since a large, cosmological neutrino background is firmly believed to exist by analogy with the observed cosmological photon background. The neutrino background has not been directly observed, but