We explore the covariance of redshift-space matter power spectra after a standard density-field reconstruction. We derive perturbative formula of the covariance at the tree-level order and find that the amplitude of the off-diagonal components from the trispectrum decreases by reconstruction. Using a large set of $N$-body simulations, we also find the similar reduction of the off-diagonal components of the covariance and thereby the signal-to-noise ratio (S/N) of the post- reconstructed (post-rec) power spectra significantly increases compared to the pre-reconstructed (pre-rec) spectra. This indicates that the information leaking to higher-order statistics come back to the two-point statistics by reconstruction. Interestingly, the post-rec spectra have higher S/N than the linear spectrum with Gaussian covariance when the scale of reconstruction characterized with the smoothing scale of the shift field is below $\sim 10h^{-1}$Mpc where the trispectrum becomes negative. We demonstrate that the error of the growth rate estimated from the monopole and quadrupole components of the redshift-space matter power spectra significantly improves by reconstruction. We also find a similar improvement of the growth rate even when taking into account the super-sample covariance, while the reconstruction cannot correct for the field variation of the super-sample modes.

中文翻译：

---

重构后红移空间物质功率谱的协方差

在标准密度场重建之后，我们探索了红移空间物质功率谱的协方差。我们推导了树级顺序的协方差的摄动公式，并发现通过重建，来自三光谱的非对角线分量的幅度减小了。使用大量的$ñ$体仿真中，我们还发现协方差的非对角线分量的相似减少，因此，与重建后（后记录）功率谱相比，信噪比（S / N）显着增加。预重构（pre-rec）光谱。这表明泄漏到高阶统计信息的信息通过重构又回到了两点统计。有趣的是，当以移位场的平滑尺度为特征的重建尺度低于时，记录后谱的信噪比高于具有高斯协方差的线性谱。$〜10H^{-\mathrm{1个}}$MPC，其中三光谱变为负值。我们证明，通过重建，从红移空间物质功率谱的单极和四极分量估计的增长率的误差显着提高。即使在考虑到超样本协方差的情况下，我们也发现增长率有类似的提高，而重建无法校正超级样本模式的场变化。