Long-range interactions between dark-matter particles in a model with a cosmological, spontaneously-broken chiral symmetry

In a cosmological model with a chiral symmetry, there are two, dynamically-related spin-zero fields, a scalar φ and a pseudoscalar b. These fields have self-interactions. Spontaneous symmetry breaking results in a very massive scalar particle with m(φ) ≅ 5 x 10(11) GeV, and a nearly massless, (Goldstone-like) pseudoscalar particle with 0 < m(b) ≲ 2.7 x 10(-6) eV. One or both particles can be part of dark matter. There are coherent long-range interactions (at range ∼ 1/(mb) ≳ 10 cm), from exchange of a b particle between a pair of b particles, a pair of 0 particles, and between a 0 and a b. We compare the strength of potentials for the different pairs to the corresponding gravitational potentials (within the same range ∼ 1/m(b)), and show that the new force dominates between a b pair, that gravitation dominates between a 0 pair, and that the potentials are comparable for a φ-b pair. The new interaction strength between a b pair is comparable to the gravitational interaction between a 0 pair; its possibly greater coherent effect originates in the possibility that the number density of a very light b can be greater than that of a massive φ. We consider these results in the context of recent speculations concerning possible effects of special forces between dark-matter particles on certain galactic, and inter-galactic, properties.