Nonrelativistic formation of scalar clumps as a candidate for dark matter

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 stabilized 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. The shape and the scaling laws of the clumps depend on their formation mechanism. When the tachyonic phase takes place, the core density of the clumps is uniquely determined by the energy density at the beginning of the instability. On the other hand, for axion monodromy, the core density scales with the soliton mass and radius. This difference comes from the crucial role that the quantum pressure plays in both the parametric resonance in the linear regime and in the nonlinear formation regime of static scalar solitons. 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 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. We find that the formation redshift of the scalar clumps can span a large range in the radiation era; the associated background temperature can vary from 10 eV to 10 5 GeV, and the scalar-field mass from 10 −26 GeV to 10 GeV.

Beyond Schrödinger-Poisson: nonrelativistic effective field theory for scalar dark matter

“…They are approximate, time-dependent solitons of the relativistic theory. Such solitons are relevant in many cosmological contexts, both in the early and contemporary universe (for example, see [15,37,55,[63][64][65][66][67][68][69][70][71][72][73][74]). They owe their localization to gravitational interactions [59,[75][76][77], or self-interactions [16,52,78] or a combination of both.…”

Precision Measurement Noise Asymmetry and Its Annual Modulation as a Dark Matter Signature

“…[16]). In this case, galactic structure formation would occur as per conventional cold dark matter theory [6,27].…”

“…A formation of DM clumps in the radiation era has been analyzed recently in Ref. [27]. The clump formation requires non-linear self-interactions of the scalar DM field.…”

“…The clump mass-radius relation follows a power law, M ∼ R n , where the power n = 3, 4, 5 depends on the details of the formation mechanisms and the self-interaction potential. Because of finite-size effects, these dark matter clumps are shown [27] to evade the microlensing constraints [28].…”

Testing Screened Modified Gravity

“…More generally, (pseudo-)scalars could play the role of dark matter thanks to the misalignment mechanism, i.e. they behave as oscillating fields, as long as their mass m is low, typically m < ∼ 1 eV [22][23][24]. On the late acceleration side, the cosmological constant is certainly a strong contender albeit a very frustrating one.…”