利用Rees-Sciama效应与弱透镜的互相关探讨中微子质量
Probing the Neutrino Mass through the Cross Correlation between the Rees-Sciama Effect and Weak Lensing
摘要：
宇宙学在确定中微子质量方面起着基础性的作用，因此也决定了它的质量等级，因为大质量中微子一旦成为非相对论性的，就会在背景和微扰水平上对宇宙中的总物质密度做出贡献。在非相对论性跃迁之后，涨落在尺度$k\gg k_{fs}$上破碎。因此，总物质中缺失的涨落被印刻在大尺度结构上，比如在尺度$k\gg k_{fs}$上物质功率谱$ΔP/P\approx -8f_ν$的抑制。在本文中，而不是考虑线性微扰理论，这是很好地理解在中微子的存在下，我们建议使用的Rees-Sciama效应和弱透镜之间的交叉关联探测中微子质量。在小尺度下，密度对比度比背景比例因子$δ\sim a$增长得更快，这使得$Φ' \propto \mathcal{H}δd\ln (δ/a)/d\ln a$上的符号翻转，这仅发生在非线性区域中。通过对浅、深弱透镜观测的假设，我们证明了Rees-Sciama效应和弱透镜效应互功率谱中的翻转尺度依赖于中微子质量。我们的分析表明，深测量具有较大的信噪比$S/N\sim 160$。最后，我们利用Fisher信息矩阵预测了中微子质量的约束。
英文摘要：
Cosmology plays a fundamental role to determine the neutrino mass, therefore also to determine its mass hierarchy, since the massive neutrino contributes to the total matter density in the Universe at the background and perturbation levels, once it becomes non-relativistic. After the non-relativistic transition the fluctuations are smashed out at the scales $k\gg k_{fs}$. Therefore, the missing fluctuation in the total matter is imprinted on the large scale structure, say the suppression of the matter power spectrum $ΔP/P\approx -8f_ν$ at the scales $k\gg k_{fs}$. In this paper, instead of considering the linear perturbation theory, which is well understood in the presence of neutrino, we propose to use the cross correlation between the Rees-Sciama effect and weak lensing to probe the neutrino mass. At the small scales, the density contrast grows faster than the background scale factor $δ\sim a$, that makes a sign flipping on $Φ' \propto \mathcal{H}δd\ln (δ/a)/d\ln a$, which happens only in the non-linear regime. We show that the flipping scale in the cross power spectrum between the Rees-Sciama effect and weak lensing depends on the neutrino mass by assuming the shallow and deep weak lensing surveys. Our analysis shows that the Deep survey has larger signal-to-noise ratio $S/N\sim 160$. Finally, we use the Fisher information matrix to forecast constraint on the neutrino mass.
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