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 $\phi$ and a pseudoscalar $b$. These fields have self-interactions. Spontaneous symmetry breaking results in a very massive scalar particle with $m_\phi\cong 5 \times 10^{11}\GeV$, and a nearly massless, (Goldstone-like) pseudoscalar particle with $0< m_b <~ 2.7\times 10^{-6}\eV$. One or both particles can be part of dark matter. There are coherent long-range interactions (at range $\sim 1/m_b \simgt 10\cm$), from exchange of a $b$ particle between a pair of $b$ particles, a pair of $\phi$ particles, and between a $\phi$ and a $b$. We compare the strength of potentials for the different pairs to the corresponding gravitational potentials (within the same range $\sim 1/m_b$), and show that the new force dominates between a b pair, that gravitation dominates between a $\phi$ pair, and that the potentials are comparable for a $\phi$-$b$ pair. The new interaction strength between a $b$ pair is comparable to the gravitational interaction between a $\phi$ 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 $\phi$. 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. 
Saul Barshay and Georg Kreyerhoff