To combine information from measurements of the redshift-space power spectrum from spectroscopic data with angular weak lensing, galaxy clustering, and galaxy-galaxy lensing power spectra from photometric surveys (i.e., the $3\times 2$ point statistics), we must account for the covariance between the two probes. Currently any covariance between the two types of measurements is neglected as existing photometric and spectroscopic surveys largely probe different cosmological volumes. This will cease to be the case as data arrive from Stage-IV surveys. In this paper we derive an analytic expression for the covariance between photometric two-dimensional angular power spectra and the three-dimensional redshift-space power spectrum for Gaussian fields under the plane-parallel approximation. We find that the two probes are covariant on large radial scales, but because this covariance only appears over a small fraction of the total Fourier space coverage of the two types of probes, we forecast that it is safe to neglect this covariance when performing cosmological parameter inference.

中文翻译：

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光度和光谱两点统计的协方差：对宇宙学参数推断的影响

将来自光谱数据的红移空间功率谱测量信息与来自光度测量的角度弱透镜、星系集群和星系-星系透镜功率谱（即，$3\times 2$点统计），我们必须考虑两个探针之间的协方差。目前，由于现有的光度学和光谱学调查在很大程度上探测不同的宇宙体积，因此忽略了两种测量类型之间的任何协方差。随着第四阶段调查的数据到来，这种情况将不再存在。在本文中，我们推导了平面平行近似下高斯场光度二维角功率谱与三维红移空间功率谱之间协方差的解析表达式。我们发现这两种探针在大径向尺度上是协变的，但是因为这种协方差只出现在两种探针的总傅里叶空间覆盖范围的一小部分，我们预测在执行宇宙学参数时忽略这种协方差是安全的推理。