Abstract
Neutrinos can gain mass from coupling to an ultralight field in slow roll. When such a field is displaced from its minimum, its vev acts just like the Higgs vev in spontaneous symmetry breaking. Although these masses may eventually vanish, they do it over a very long time. The theory is technically natural, with the ultralight field-dependent part being the right-handed Majorana mass. The mass variation induced by the field correlates with the cosmological evolution. The change of the mass term changes the mixing matrix, and therefore suppresses the fraction of sterile neutrinos at earlier times and increases it at later times. Since the issue of quantum gravity corrections to field theories with large field variations remains open, this framework may give an observational handle on the Weak Gravity Conjecture.
Highlights
Neutrinos can gain mass from coupling to an ultralight field in slow roll
If dark energy is not constant, we can accommodate it in field theory as a quantum field with an extremely flat potential, whose vacuum expectation value is displaced from the minimum
If dark energy is really something like quintessence, the problem would become even deeper, since in addition to explaining the smallness of vacuum energy one would need to explain the origin of the ultra-low scales governing the quintessence sector
Summary
Neutrinos can gain mass from coupling to an ultralight field in slow roll. When such a field is displaced from its minimum, its vev acts just like the Higgs vev in spontaneous symmetry breaking. A quintessence field can directly couple to neutrinos and remain light enough to continue behaving as dark energy even when quantum corrections are accounted for [7]. While coupled quintessence fields can mediate a long range force between neutrinos, the resulting bounds are feeble at present.
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