USES OF A SMALL FIELD VALUE WHICH FALLS FROM A METASTABLE MAXIMUM OVER COSMOLOGICAL TIMES
Abstract
We consider a small, metastable maximum vacuum expectation value b0 of order of a few eV, for a pseudoscalar Goldstone-like field, which is related to the scalar inflaton field ϕ in an idealized model of a cosmological, spontaneously-broken chiral symmetry. The b field allows for relating semi-quantitatively three distinct quantities in a cosmological context.
(a) A very small, residual vacuum energy density or effective cosmological constant of 
, for λ ~ 3×10-14, the same as an empirical inflaton self-coupling.
(b) A tiny neutrino mass, less than b0.
(c) A possible small variation downward of the proton to electron mass ratio over cosmological time. The latter arises from the motion downward of the b field over cosmological time, toward a nonzero value. Such behavior is consistent with an equation of motion.
We argue that hypothetical b quanta, potentially inducing new long-range forces, are absent, because of negative, effective squared mass in an equation of motion for b-field fluctuations. The assumed flatness of a potential maximum involves a small inverse-time parameter μ ≪ 1/t0, where t0 is the present age of the universe.
