  We present and discuss the properties and the main results of a cosmological
model with a spontaneously-broken chiral symmetry. The model contains and
relates dynamically, two spin-zero fields. The scalar field can provide the
dynamical basis for inflation in the early universe. The pseudoscalar,
Goldstone field can provide an early, small residual vacuum energy density, the
absolute value of which we estimate to be similar to the present, empirically
small vacuum energy density. The small energy scale for this effective
cosmological constant is estimated separately, by relating it dynamically to
the empirical, small scale of neutrino mass. CP invariance is broken
spontaneously. This provides a natural basis for the early generation of an
antineutrino-neutrino asymmetry, whose magnitude we estimate, and find to be
significant.
