Cosmological parameter estimation from forthcoming experiments promise to reach much greater precision than current constraints. As statistical errors shrink, the required control over systematic errors increases. Therefore, models or approximations that were sufficiently accurate so far, may introduce significant systematic biases in the parameter best-fit values and jeopardize the robustness of cosmological analyses. We present a general expression to estimate a priori the systematic error introduced in parameter inference due to the use of insufficiently good approximations in the computation of the observable of interest or the assumption of an incorrect underlying model. Although this methodology can be applied to measurements of any scientific field, we illustrate its power by studying the effect of modeling the angular galaxy power spectrum incorrectly. We also introduce Multi_CLASS, a new, public modification of the Boltzmann code CLASS, which includes the possibility to compute angular cross-power spectra for two different tracers. We find that significant biases in most of the cosmological parameters are introduced if one assumes the Limber approximation or neglects lensing magnification in modern galaxy survey analyses, and the effect is in general larger for the multi-tracer case, especially for the parameter controlling primordial non-Gaussianity of the local type, $f_{\rm NL}$.

中文翻译：

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注意常用的近似值。第二部分。估计最佳拟合参数的系统偏差

来自即将进行的实验的宇宙学参数估计有望达到比当前限制更高的精度。随着统计误差的缩小，对系统误差的控制要求增加。因此，迄今为止足够准确的模型或近似值可能会在参数最佳拟合值中引入显着的系统偏差，并危及宇宙学分析的稳健性。我们提出了一个通用表达式来先验地估计由于在计算感兴趣的可观察量或不正确的基础模型的假设中使用不够好的近似值而在参数推断中引入的系统误差。虽然这种方法可以应用于任何科学领域的测量，我们通过研究错误地模拟角星系功率谱的影响来说明它的功率。我们还介绍了 Multi_CLASS，这是对 Boltzmann 代码 CLASS 的一种新的公开修改，其中包括计算两种不同示踪剂的角交叉功率谱的可能性。我们发现，如果在现代星系调查分析中假设采用 Limber 近似或忽略透镜放大倍数，大多数宇宙学参数都会引入显着偏差，并且对于多示踪剂的情况，影响通常更大，特别是对于控制原始非的参数。 -局部类型的高斯性，$f_{\rm NL}$。