Non-Relativistic Formation of Scalar Clumps as a Candidate for Dark Matter

TL;DR

This paper introduces a novel mechanism for dark matter clump formation during the radiation era via scalar field instabilities, leading to a wide range of clump sizes that could serve as dark matter candidates.

Contribution

It proposes a new formation process for scalar dark matter clumps based on instabilities from negative sound speed squared in a nonrelativistic scalar fluid.

Findings

Scalar clumps range from atomic to galactic scales.

Clumps form through tachyonic and parametric resonance instabilities.

Clumps are beyond microlensing detection due to finite-size effects.

Abstract

We propose a new mechanism for the formation of dark matter clumps in the radiation era. We assume that a light scalar field is decoupled from matter and oscillates harmonically around its vacuum expectation value. We include self-interactions and consider the nonrelativistic regime. The scalar dynamics are described by a fluid approach where the fluid pressure depends on both quantum and self-interaction effects. When the squared speed of sound of the scalar fluid becomes negative, an instability arises and the fluctuations of the scalar energy-density field start growing. They eventually become nonlinear and clumps form. Subsequently, the clumps aggregate and reach a universal regime. Afterwards, they play the role of cold dark matter. We apply this mechanism first to a model with a negative quartic term stabilised by a positive self-interaction of order six, and then to axion monodromy, where a subdominant cosine potential corrects a mass term. In the first case, the squared speed of sound becomes negative when the quartic term dominates, leading to a tachyonic instability. For axion monodromy, the instability starts very slowly after the squared speed of sound first becomes negative and then oscillates around zero. Initially the density perturbations perform acoustic oscillations due to the quantum pressure. Eventually, they start growing exponentially due to a parametric resonance. In both scenarios, the scalar-field clumps span a wide range of scales and masses, running from the size of atoms to that of galactic molecular clouds, and from $10^{-3} \, {\rm gram}$ to thousands of solar masses. Because of finite-size effects, both from the source and the lens, these dark matter clumps are far beyond the reach of microlensing observations.