Probing the Anisotropy and Non-Gaussianity in the Redshift Space through the Conditional Moments of the First Derivative

Abstract

Focusing on the redshift space observations with plane-parallel approximation and relying on the rotational dependency of the general definition of excursion sets, we introduce the so-called conditional moments of the first derivative ($cmd$) measures for the smoothed matter density field in three dimensions. We derive the perturbative expansion of $cmd$ for the real space and redshift space where peculiar velocity disturbs the galaxies' observed locations. Our criteria can successfully recognize the contribution of linear Kaiser and Finger-of-God effects. Our results demonstrate that the $cmd$ measure has significant sensitivity for pristine constraining the redshift space distortion parameter $\beta =f/b$ and interestingly, the associated normalized quantity in the Gaussian linear Kaiser limit has only $\beta$ dependency. Implementation of the synthetic anisotropic Gaussian field approves the consistency between the theoretical and numerical results. Including the first-order contribution of non-Gaussianity perturbatively in the $cmd$ criterion implies that the N-body simulations for the Quijote suite in the redshift space have been mildly skewed with a higher value for the threshold greater than zero. The non-Gaussianity for the perpendicular direction to the line of sight in the redshift space for smoothing scales $R\gtrsim 20$ Mpc h${}^{-1}$ is almost the same as the real space. In contrast, the non-Gaussianity along the line of sight direction in redshift space is magnified. The Fisher forecasts indicate an almost significant enhancement in constraining the cosmological parameters, ${\Omega }_m$, ${\sigma }_8$, and $n_s$ when using $cmd+cr$ jointly.

arXiv comment17 pages and 9 figures; Matched to the accepted format, major revision including the generalization of morphological measures and Halo bias

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• Cosmic Strings-induced CMB anisotropies in light of Weighted Morphology
• Impact of Redshift Space Distortion on Persistent Homology of cosmic matter density field
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