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.

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

References in corpus (18)

• Is the Observable Universe Consistent with the Cosmological Principle?
• Fast likelihood-free cosmology with neural density estimators and active learning
• Euclid: Forecasts from redshift-space distortions and the Alcock-Paczynski test with cosmic voids
• Quantifying the Redshift Space Distortion of the Bispectrum I: Primordial Non-Gaussianity
• Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?
• Tensor Minkowski Functionals for random fields on the sphere
• Local Anisotropy of Fluids using Minkowski Tensors
• Quantifying the Redshift Space Distortion of the Bispectrum II: Induced Non-Gaussianity at Second Order Perturbation
• Probing massive neutrinos with the Minkowski functionals of large-scale structure
• The Hot and Cold Spots in Five-Year WMAP Data
• Level Crossing Analysis of Cosmic Microwave Background Radiation: A method for detecting cosmic strings
• Halo assembly bias from a deep learning model of halo formation
• Cosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Expansion History using the Genus Amplitude as a Standard Ruler
• Cosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Shape of the Matter Power Spectrum
• Minkowski Tensors in Redshift Space -- Beyond the Plane Parallel Approximation
• The statistics of peaks of weakly non-Gaussian random fields: Effects of bispectrum in two- and three-dimensions
• Quantifying the redshift space distortion of the bispectrum III : Detection prospects of the multipole moments
• The effects of peculiar velocities on the morphological properties of large-scale structure

Cited by in corpus (4)

• Imprint of massive neutrinos on Persistent Homology of large-scale structure
• Cosmic Strings-induced CMB anisotropies in light of Weighted Morphology
• Impact of Redshift Space Distortion on Persistent Homology of cosmic matter density field
• Quantifying Weighted Morphological Content of Large-Scale Structures via Simulation-Based Inference