We study the importance of gravitational lensing in modelling the number counts of galaxies for the first time in spectroscopic surveys. We confirm previous results for photometric surveys, showing that lensing cannot be neglected in a survey like LSST since it would infer a significant shift of standard cosmological parameters. For a spectroscopic survey like SKA2, we find that neglecting lensing in the monopole, quadrupole and hexadecapole of the correlation function can also induce an important shift of cosmological parameters. For ΛCDM parameters, the shift is moderate, of the order of 0.6σ or less. However, for a model-independent analysis, that measures the growth rate of structure in each redshift bins, neglecting lensing introduces a shift of up to 2.3σ at high redshift. Since the growth rate is directly used to test the theory of gravity, such a strong shift would wrongly be interpreted as the breakdown of General Relativity. This shows the importance of including lensing in the analysis of future surveys. For a survey like DESI, we find on the other hand that lensing is not important, mainly due to the value of the magnification bias parameter of DESI, s(z), which strongly reduces the lensing contribution at high redshift. This result relies on our theoretical modelling of s(z) in DESI and should therefore be confirmed with measurements of s(z) in simulations. We also propose a way of improving the analysis of spectroscopic surveys, by including the cross-correlations between different redshift bins (which is neglected in spectroscopic surveys) from the spectroscopic survey or from a different photometric sample. We show that including the cross-correlations in the SKA2 analysis does not improve the constraints. On the other hand replacing the cross-correlations from SKA2 by cross-correlations measured with LSST improves the constraints by 10% to 20%. The marginal improvement is mainly due to the density correlations between nearby bins and, therefore, does not strongly depend on our knowledge of the magnification bias. Interestingly, for standard cosmological parameter estimation, the photometric survey LSST in its 12 redshift bin configuration and the spectroscopic SKA2 survey are highly complementary, since they are affected by different degeneracies between parameters: LSST yields the tightest constraints on Ω_cdm, h and n _s, while SKA2 better constrains Ω_baryon, A _s and the bias.

我们首次在光谱调查中研究了引力透镜在模拟星系数量方面的重要性。我们确认了之前的光度测量结果，表明在像 LSST 这样的测量中不能忽略透镜，因为它会推断标准宇宙学参数的显着变化。对于像 SKA2 这样的光谱调查，我们发现忽略相关函数的单极子、四极子和十六极子中的透镜也会引起宇宙学参数的重要变化。对于 ΛCDM 参数，偏移适中，约为 0.6σ 或更小。然而，对于独立于模型的分析，测量每个红移箱中结构的增长率，忽略透镜会在高红移处引入高达 2.3σ 的位移。由于增长率是直接用来检验引力理论的，如此强烈的转变会被错误地解释为广义相对论的崩溃。这表明在未来调查的分析中包含镜头的重要性。对于DESI这样的调查，另一方面我们发现透镜并不重要，主要是由于DESI的放大偏差参数的值，s ( z )，这大大降低了高红移时的透镜效应。这个结果依赖于我们在 DESI中s ( z ) 的理论模型，因此应该通过s ( z) 在模拟中。我们还提出了一种改进光谱调查分析的方法，包括来自光谱调查或不同光度测量样本的不同红移箱（在光谱调查中被忽略）之间的互相关。我们表明，在 SKA2 分析中包含互相关并不能改善约束。另一方面，用 LSST 测量的互相关替换来自 SKA2 的互相关将约束提高 10% 到 20%。边际改善主要是由于附近 bin 之间的密度相关性，因此并不强烈依赖于我们对放大偏差的了解。有趣的是，对于标准的宇宙学参数估计，_CDM，ħ和Ñ _小号，而更好SKA2约束Ω_重子，甲 _小号和偏置。