In the era of precision cosmology, establishing the correct magnitude of statistical errors in cosmological parameters is of crucial importance. However, widely used approximations in galaxy surveys analyses can lead to parameter uncertainties that are grossly mis-estimated, even in a regime where the theory is well understood (e.g., linear scales). These approximations can be introduced at three different levels: in the form of the likelihood, in the theoretical modelling of the observable and in the numerical computation of the observable. Their consequences are important both in data analysis through e.g., Markov Chain Monte Carlo parameter inference, and when survey instrument and strategy are designed and their constraining power on cosmological parameters is forecasted, for instance using Fisher matrix analyses. In this work, considering the galaxy angular power spectrum as the target observable, we report one example of approximation for each of such three categories: neglecting off-diagonal terms in the covariance matrix, neglecting cosmic magnification and using the Limber approximation on large scales. We show that these commonly used approximations affect the robustness of the analysis and lead, perhaps counter-intuitively, to unacceptably large mis-estimates of parameters errors (from few~$10\%$ up to few~$100\%$) and correlations. Furthermore, these approximations might even spoil the benefits of the nascent multi-tracer and multi-messenger cosmology. Hence we recommend that the type of analysis presented here should be repeated for every approximation adopted in survey design or data analysis, to quantify how it may affect the results. To this aim, we have developed \texttt{Multi\_CLASS}, a new extension of \texttt{CLASS} that includes the angular power spectrum for multiple (galaxy and other tracers such as gravitational waves) populations.

中文翻译：

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注意常用的近似值。第一部分. 预测错误

在精密宇宙学时代，确定宇宙学参数统计误差的正确大小至关重要。然而，在星系调查分析中广泛使用的近似值会导致参数的不确定性，这些不确定性被严重错误地估计，即使在理论很好理解的情况下（例如，线性尺度）也是如此。这些近似值可以在三个不同的层次上引入：以似然的形式、在可观察量的理论建模中和在可观察量的数值计算中。它们的结果在通过例如马尔可夫链蒙特卡罗参数推断进行的数据分析中以及在设计调查工具和策略以及预测它们对宇宙学参数的约束力（例如使用费舍尔矩阵分析）时都很重要。在这项工作中，考虑到星系角功率谱作为目标可观察量，我们报告了这三类中每一种的一个近似示例：忽略协方差矩阵中的非对角项、忽略宇宙放大率和在大尺度上使用 Limber 近似。我们表明，这些常用的近似值会影响分析的稳健性，并可能与直觉相反地导致对参数误差（从很少~$10\%$ 到很少~$100\%$）和相关性的不可接受的大错误估计。此外，这些近似甚至可能破坏新生的多示踪剂和多信使宇宙学的好处。因此，我们建议应针对调查设计或数据分析中采用的每个近似值重复此处介绍的分析类型，以量化它对结果的影响。为了这个目标，