Fluid Dark Matter

TL;DR

We address the small-scale structure problems of cold dark matter by proposing dark matter as a gravitationally produced self-interacting scalar field with a potential that is quartic at large field values and quadratic at small values, $V(y)=(m^2/2) y^2 + (K/q)|y|^q$ with $q>2$. In the subdominant-anharmonic regime the field behaves as an ideal, nonrelativistic fluid with pressure $p_y$ as a function of density $\rho_y$, yielding a density-dependent Jeans length $\lambda_J$ set by $c_s = \sqrt{d p_y/d\rho_y}$ and producing core radii $r_c$ and possible solid-body rotation in halos; structure formation also requires a transfer-function cutoff at $k_c$ determined by $k_c t_{eq} z_{eq} \approx \pi$. The analysis highlights an inflationary origin for dark matter, differentiates the fluid picture from self-interacting gas models, and discusses observational consequences for halo cores, dwarf galaxies, and the low-mass end of the primordial fluctuation spectrum, including potential isocurvature or reduced small-scale power scenarios depending on parameters. This framework connects early-Universe inflation, classical field dynamics, and galaxy-scale observations, offering a mechanism to reconcile halo cores with inflation-based dark matter and to tune small-scale structure via the potential form and the Jeans length.

Abstract

Dark matter modeled as a classical scalar field that interacts only with gravity and with itself by a potential that is close to quartic at large field values and approaches a quadratic form when the field is small would be gravitationally produced by inflation and at the present epoch could act like an ideal fluid with pressure that is a function only of the mass density. This could have observationally interesting effects on the core radii and solid body rotation of dark matter halos and on the low mass end of the primeval mass fluctuation power spectrum.