CP noninvariance and an effective cosmological constant: the energy   density in a pseudoscalar field which arises from a cosmological,   spontaneously-broken chiral symmetry
  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. 
Saul Barshay and Georg Kreyerhoff