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. (1) A very small, residual vacuum energy density or effective cosmological constant of ~ lambda b04 ~ 2.7 x 10-47GeV4, for lambda ~ 3 x 10-14, the same as an empirical inflaton self-coupling. (2) A tiny neutrino mass, less then b0. (3) 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 limiting value as t ∞. 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.