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, dynamicallyrelated 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 mφ ∼= 5×1011 GeV, and a nearly massless, (Goldstonelike) pseudoscalar particle with 0 < mb < ∼ 2.7×10−6 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 φ particles, and between a φ and a b. We compare the strength of potentials for the different pairs to the corresponding gravitational potentials (within the same range ∼ 1/mb), and show that the new force dominates between a b pair, that gravitation dominates between a φ 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 φ 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. In this note, we point out the strength, and certain possible physical consequences, of coherent long-range interactions which can exist only between darkmatter particles. These interactions arise naturally in a model with a cosmological, spontaneously-broken chiral symmetry [1, 2]. There have been a number of speculations about such forces. For example, one motivation [3] has been to