Future galaxy surveys will provide accurate measurements of the matter power spectrum across an unprecedented range of scales and redshifts. The analysis of these data will require to accurately model the imprint of non-linearities on the matter density field, which induces a non-Gaussian contribution to the data covariance. As the imprint of non-linearities is cosmology dependent, a further complication arises from accounting for the cosmological dependence of the non-Gaussian part of the covariance. Here, we study this using a dedicated suite of N-body simulations, the Dark Energy Universe Simulation - Parallel Universe Runs (DEUS-PUR) $Cosmo$. These consist of 512 realizations for 10 different cosmologies where we vary the matter density $\Omega_m$, the amplitude of density fluctuations $\sigma_8$, the reduced Hubble parameter $h$ and a constant dark energy equation of state $w$ by approximately $10\%$. We use these data to evaluate the first and second derivatives of the power spectrum covariance with respect to a fiducial $\Lambda$CDM cosmology. We find that the variations can be as large as $150\%$ depending on the scale, redshift and model parameter considered. Using a Fisher matrix approach, we evaluate the impact of using a covariance estimated at a fiducial model rather than the true underlying cosmology. We find that the estimated $1\sigma$ errors are affected at approximately $5\%$, $20\%$, $50\%$ and $120\%$ level when assuming non-fiducial values of $h$, $w$, $\Omega_m$ and $\sigma_8$ respectively. These results suggest that the use of cosmology-dependent covariances is key for precision cosmology.

中文翻译：

---

来自 DEUS-PUR 宇宙模拟的物质功率谱协方差的宇宙学模型参数依赖性

未来的星系调查将在前所未有的尺度和红移范围内提供对物质功率谱的准确测量。对这些数据的分析将需要对物质密度场上的非线性印记进行准确建模，这会导致对数据协方差的非高斯贡献。由于非线性的印记是与宇宙学相关的，因此解释协方差的非高斯部分的宇宙学相关性会产生进一步的复杂性。在这里，我们使用一组专用的 N 体模拟来研究这个问题，即暗能量宇宙模拟 - 平行宇宙运行 (DEUS-PUR) $Cosmo$。这些由 10 种不同宇宙学的 512 种实现组成，其中我们改变了物质密度 $\Omega_m$、密度波动幅度 $\sigma_8$，将哈勃参数 $h$ 和状态 $w$ 的恒定暗能量方程减少了大约 $10\%$。我们使用这些数据来评估功率谱协方差相对于基准 $\Lambda$CDM 宇宙学的一阶和二阶导数。我们发现，根据所考虑的尺度、红移和模型参数，变化可能高达 $150\%$。使用Fisher 矩阵方法，我们评估使用在基准模型而不是真实基础宇宙学中估计的协方差的影响。我们发现，当假设非基准值为 $h$、$w$、$ 时，估计的 $1\sigma$ 误差在大约 $5\%$、$20\%$、$50\%$ 和 $120\%$ 水平受到影响\Omega_m$ 和 $\sigma_8$ 分别。这些结果表明，使用与宇宙学相关的协方差是精确宇宙学的关键。