  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.
