AI 中文总结
本研究利用Planck CMB数据及BAO、SNIa几何探针，推导含各向异性贡献的CMB温度协方差矩阵，对自旋1超轻暗物质的质量给出宇宙学约束，并指出混合暗物质模型的特征信号值得专门搜寻。
AI 中文摘要
我们利用Planck宇宙微波背景（CMB）数据以及来自重子声学振荡（BAO）和Ia型超新星（SNIa）的几何探针，对由质量为$m_{\rm A}$的矢量场描述的自旋1超轻暗物质（VFDM）给出了宇宙学约束。一项关键的理论成果是推导了完整的CMB温度协方差矩阵，其中包括由背景矢量场的择优方向诱导的对角和非对角各向异性贡献。我们首先利用协方差的对角部分结合CMB引力透镜对该模型进行约束；耦合多极矩满足$Δ\rellin{2,4}$的非对角项可能会使透镜重建产生偏差，但这种偏差仅出现在Planck似然函数未包含的极低多极矩（$L={2,4}$）处。我们同时考虑了纯VFDM情形和以$f=Ω_{\rm A}/(Ω_{\rm A}+Ω_{\rm cdm})$为特征占比的VFDM+冷暗物质（CDM）混合情形，得到纯情形下$\nLog_{10}(m_{\rm A}/\rmeV)>-24.07$（95%置信水平），混合情形下$f$与$m_{\rm A}$存在明显相关性，占比越小允许的质量越轻；标准宇宙学参数与ΛCDM模型保持完全一致。针对非对角贡献，我们推导了对应的双极球谐函数（BipoSH）系数，并利用我们的最佳拟合值和约束边界预测了其振幅。虽然在当前Planck数据下纯VFDM情形中的各向异性信号难以探测，但VFDM+CDM混合模型可在一定多极矩范围内产生达到或超过Planck灵敏度的信号，这为专门搜寻这一特征信号提供了动机。
英文摘要
We present cosmological constraints on spin-1 ultralight dark matter, described by a vector field (VFDM) with mass $m_{\rm A}$, using Planck CMB data and geometrical probes from BAO and SNIa. A key theoretical result is the derivation of the full CMB temperature covariance matrix, including both diagonal and off-diagonal anisotropic contributions induced by the preferred direction of the background vector field. We first constrain the model using the diagonal part of the covariance, together with CMB lensing; the off-diagonal terms, which couple multipoles with $Δ\ell\in\{2,4\}$, could bias lensing reconstruction, but only at very low multipoles ($L=\{2,4\}$) not included in the Planck likelihood. We consider both a pure VFDM scenario and a mixed VFDM+CDM scenario, characterized by the fraction $f=Ω_{\rm A}/(Ω_{\rm A}+Ω_{\rm cdm})$, obtaining $\log_{10}(m_{\rm A}/\mathrm{eV})>-24.07$ (95\% C.L.) in the pure case, and a clear correlation between $f$ and $m_{\rm A}$ in the mixed case, with smaller fractions allowing lighter masses; standard cosmological parameters remain fully consistent with $Λ$CDM. For the off-diagonal contributions, we derive the corresponding Bipolar Spherical Harmonic (BipoSH) coefficients and predict their amplitude using our best-fit and bounds. While the anisotropic signal is difficult to detect in the pure VFDM scenario with current Planck data, mixed VFDM+CDM models can produce signals at, or above, Planck sensitivity over a range of multipoles, motivating dedicated searches for this characteristic signature.
Comments14 pages, 5 figures
