Some theoretical models for the early Universe predict a spike-type enhancement in the primordial power spectrum on a small scale, which would result in forming early-formed dark matter halos (EFHs). Some recent studies have claimed to have placed limits on such small scales, which, however, involve uncertainties, such as the physics of substructures and the halo-galaxy relations. In this work, we study the cosmic microwave background (CMB) lensing effect, considering the existence of EFHs, and investigate the potential to probe the EFHs and the primordial perturbations on scales smaller than 1 Mpc, complementing these previous studies. We numerically calculate the angular power spectrum of the lensing potential and the lensed CMB anisotropy of temperature, E-mode, and B-mode polarization, including the nonlinear effects of EFHs. We find the possibility that the lensed CMB temperature anisotropy is significantly enhanced on small scales, $\ell >1000$, and could be tested by component decomposition of observed signals through multifrequency observations. Through the calculation with different models of the spiky-type power spectrum, we demonstrate that the accurate measurements of the CMB lensing effect would provide insight into the abundance of EFHs within the limited mass range around ${10}^{11}{M}_{\odot }$ and the primordial power spectrum on the limited scales around $k\sim 1{\mathrm{Mpc}}^{-1}$. In particular, we find that the existence of such EFHs can amplify the lensed anisotropy of CMB B-mode polarization even on large scales, $\ell <100$, as the overall enhancement by $\sim 5\%$ level compared to the standard structure formation model without EFHs. Therefore, future CMB measurements, such as the LiteBIRD satellite, can probe the existence of the EFHs and the spike-type primordial power spectrum through the precise measurement of the large-scale CMB B-mode polarization.

中文翻译：

---

早期形成的暗物质晕的 CMB 透镜效应

早期宇宙的一些理论模型预测，原始功率谱会在小范围内出现尖峰型增强，这将导致形成早期形成的暗物质晕（EFH）。最近的一些研究声称对如此小的尺度进行了限制，然而，这涉及不确定性，例如子结构的物理和晕星系关系。在这项工作中，我们考虑了 EFH 的存在，研究了宇宙微波背景 (CMB) 透镜效应，并研究了在小于 1 Mpc 的尺度上探测 EFH 和原初扰动的潜力，对之前的研究进行了补充。我们以数值方式计算了透镜势的角功率谱以及温度、E模式和B模式偏振的透镜 CMB 各向异性，包括 EFH 的非线性效应。我们发现透镜 CMB 温度各向异性有可能在小尺度上显着增强，$\ell >1000$，并且可以通过多频率观测对观测信号进行分量分解来进行测试。通过不同尖峰型功率谱模型的计算，我们证明了 CMB 透镜效应的精确测量将有助于了解 EFH 在有限质量范围内的丰度。${10}^{11}{\mathrm{中号}}_{\odot }$以及周围有限尺度上的原始功率谱$k～1{\mathrm{最大功率控制}}^{-1}$。特别是，我们发现这种 EFH 的存在甚至可以在大尺度上放大 CMB B模式偏振的透镜各向异性，$\ell <100$，作为整体增强$～5\%$与没有 EFH 的标准结构形成模型相比。因此，未来的CMB测量，例如LiteBIRD卫星，可以通过对大尺度CMB B模式偏振的精确测量来探测EFH和尖峰型原始功率谱的存在。