Cp Noninvariance and an Effective Cosmological Constant: The Energy Density in a Pseudoscalar Field Which Arises From a Cosmological, Spontaneously-Broken Chiral Symmetry

Abstract

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.

Dark-Matter Particles and Baryons From Inflation and Spontaneous Cp Violation in the Early Universe

“…Also, one can ask whether a spontaneous CP violation is related to the vacuum expectation value of a pseudoscalar field involved in the dynamics of inflation, and whether this dynamics might contain a reason for the actual, small value of the baryon to photon ratio, a few times 10 −10 (alternatively, for the empirical number of baryons, a few times 10 78 ). In this paper, we describe several properties of a model which contains a scalar inflaton field with a large vacuum expectation value [1,2] at a calculated [3,1], potential minimum, and also a related pseudoscalar field, whose small vacuum expectation value breaks CP invariance spontaneously [2]. These properties, taken together, suggest specific affirmative answers to the above questions.…”

“…An estimated order of magnitude of the time for conversion of the initial, inflaton potential ("vacuum") energy into S quanta is The above sequence for the appearance of radiation is meant to be illustrative of a possibility. Our main concerns in this paper are the creation F 1 This model [1,2] considers dark-matter particles to be not solely a somewhat massive, stable remnant of the initial radiation, whose present energy density has evolved, rather accidentally, to be about five times greater than the energy density in ordinary baryons. The model attempts to explain the latter fact in a unified way, including CP noninvariance leading to the the absolute number of baryons.…”

“…Inflation of scale by ∼ 10 26 (∼ e 60 ) rapidly expands the causal dimension to cover the dimension of about 3 cm, which corresponds to the radial size of the the region at 10 −36 s which subsequently expands to the presently observable universe. Near to the end of inflation, dark-matter particles φ (inflatons) with an estimated [2,1] …”

“…The cosmological, chiral model [2] contains a pseudoscalar field b, in addition to the scalar inflaton field φ. When the chiral symmetry is spontaneously broken at φ = φ c , the quanta of the b field are the necessary massless Goldstone bosons, [9] just as the pions are the Goldstone bosons in the σ-model for nucleon (equivalently, constituent quark) mass in low-energy particle physics.…”

“…When the chiral symmetry is spontaneously broken at φ = φ c , the quanta of the b field are the necessary massless Goldstone bosons, [9] just as the pions are the Goldstone bosons in the σ-model for nucleon (equivalently, constituent quark) mass in low-energy particle physics. [10,11] We have examined some consequences [2,12] of the hypothesis that the vacuum expectation value of the b field has a nonzero value F b . CP invariance is then spontaneously broken.…”