Repulsive Dark Matter

TL;DR

This paper proposes repulsive self-interacting bosonic dark matter, realized as quanta of a self-interacting scalar field with a quartic term, to address small-scale structure problems in ΛCDM. In the nonrelativistic limit, the condensate obeys a polytropic equation of state $p = K ρ^2$ and forms a self-gravitating core with a minimum radius $r_{c,min} = 3 a$, while in the relativistic regime the high-density EOS tends to $p ≈ ρ/3$ and the mass–coupling relation links $m$, $κ$ to the core scale via $m c^2 = \left( \frac{27 ħ^3 c^3 κ}{4 π G r_{c,min}^2} \right)^{1/4}$. The model predicts suppression of linear density fluctuations below a few Mpc and a small early-Universe contribution to $N_{eff}$ compatible with nucleosynthesis, with potential implications for galactic dynamics due to superfluid behavior. If the nonrelativistic core scale is of order 1 kpc, the corresponding energy density in these quanta would be comparable to photons in the early universe, a robust though nontrivial coincidence. The framework motivates further study of observational signatures and constraints on dark-halo cores and cosmological evolution.

Abstract

It seems necessary to suppress, at least partially, the formation of structure on subgalactic scales. As an alternative to warm or collisional dark matter, I postulate a condensate of massive bosons interacting via a repulsive interparticle potential, plus gravity. This leads to a minimum lengthscale for bound objects, and to superfluidity. Galactic dynamics may differ significantly from that of more generic dark matter in not unwelcome ways, especially in the core. Such particles can be realized as quanta of a relativistic massive scalar field with a quartic self-interaction. At high densities, the equation of state has the same form as that of an ideal relativistic gas despite the interactions. If the nonrelativistic lengthscale is of order a kiloparsec, then the energy density in these particles was comparable to that of photons at early times, but small enough to avoid conflict with primordial nucleosynthesis.