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. 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 $10^{-3} \, {\rm gram}$ 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. 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 $10 \, {\rm eV}$ to $10^5 \, {\rm GeV}$, and the scalar-field mass from ${10}^{-26}$ GeV to $10$ GeV.

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非相对论形成标量团块作为暗物质的候选者

我们提出了一种辐射时代暗物质团块形成的新机制。我们假设光标量场与物质解耦，并在其真空期望值附近发生谐波振荡。我们包括自我互动，并考虑非相对论制度。标量动力学通过流体方法来描述，其中流体压力取决于量子效应和自相互作用效应。当标量流体的声速平方变为负数时，会出现不稳定性，并且标量能量密度场的波动开始增大。它们最终变为非线性并成团。随后，团块聚集并达到普遍制度。之后，他们扮演冷暗物质的角色。我们首先将此机制应用于负六次项的模型，该模型通过正六阶的正自交互作用得到稳定，然后再应用于轴化一峰制，其中主要的余弦势校正了质量项。在第一种情况下，当四次项占优势时，声音的平方速度变为负数，从而导致速动不稳定。对于轴突单峰，在声音的平方速度首先变为负值然后在零附近振荡之后，不稳定开始非常缓慢。最初，密度扰动由于量子压力而产生声振荡。最终，由于参数共振，它们开始呈指数增长。团块的形状和比例定律取决于它们的形成机理。速激相发生时，团块的核心密度唯一地由不稳定开始时的能量密度决定。另一方面，对于轴力单峰，核心密度与孤子质量和半径成比例。这种差异来自于量子压力在静态标量孤子的线性形式和非线性形成形式中的参量共振中起着至关重要的作用。在这两种情况下，标量场团块涵盖了从原子大小到银河分子云大小以及从 这种差异来自于量子压力在静态标量孤子的线性形式和非线性形成形式中的参量共振中起着至关重要的作用。在这两种情况下，标量场团块涵盖了从原子大小到银河分子云大小以及从 这种差异来自于量子压力在静态标量孤子的线性形式和非线性形成形式中的参量共振中起着至关重要的作用。在这两种情况下，标量场团块涵盖了从原子大小到银河分子云大小以及从$ 10 ^ {-3} \，{\ rm克} $到成千上万的太阳质量。由于来自光源和透镜的有限尺寸效应，这些暗物质团块远远超出了微透镜观察的范围。我们发现在辐射时代标量块的形成红移可以跨越很大的范围。相关的背景温度可以从$ 10 \，{\ rm eV} $到$ 10 ^ 5 \，{\ rm GeV} $不等，并且标量场质量为${10}^{-26}$ 到 $10$ GeV。