Related papers: Power Spectrum, Bispectrum, 2- and 3-Point Correla…
Higher-order statistics are a useful and complementary tool for measuring the clustering of galaxies, containing information on the non-gaussian evolution and morphology of large-scale structure in the Universe. In this work we present…
The influence of large-scale density fluctuations on structure formation on small scales is described by the three-point correlation function (bispectrum) in the so-called "squeezed configurations," in which one wavenumber, say $k_3$, is…
We present the three-dimensional power spectrum of galaxy clustering using measurements of the angular correlation function from the second incremental release of the Two-Micron All Sky Survey (2MASS). The angular positions of galaxies out…
Analyses of the galaxy N-Point Correlation Functions (NPCFs) have a large number of degrees of freedom, meaning one cannot directly estimate an invertible covariance matrix purely from mock catalogs, as has been the standard approach for…
Surveys of cosmological large-scale structure (LSS) are sensitive to the presence of local primordial non-Gaussianity (PNG), and may be used to constrain models of inflation. Local PNG, characterized by fNL, the amplitude of the quadratic…
We present an optimised multipole algorithm for computing the three-point correlation function (3PCF), tailored for application to large-scale cosmological datasets. The algorithm builds on a $in\, situ$ interpretation of correlation…
This paper presents a novel perspective on correlation functions in the clustering analysis of the large-scale structure of the universe. We first recognise that pair counting in bins of radial separation is equivalent to evaluating…
Geometrical model of structure of the universe is examined to obtain analytical expression for the two points nonlinear correlation function. According to the model the objects (galaxies) are concentrated into two types of structure…
We demonstrate an approach that allows separating two-point correlations created by a Gaussian random field from correlations created by cosmic foregrounds such as polarized dust emission, gravitational lensing and other non-Gaussian…
In the inflationary cosmology it occurs frequently that the inflaton field is trapped in a local, transient minimum with non-zero vacuum energy. The difficulty regarding the curvature perturbation produced during such a stage is that…
Recently isotropic basis functions of $N$ unit vector arguments were presented; these are of significant use in measuring the N-Point Correlation Functions (NPCFs) of galaxy clustering. Here we develop the generating function for these…
The evolution of two-point space correlation function of QSOs is analyzed in the framework of the theory of the large scale structure formation. For given cosmological models the agreement between theoretical predictions and observational…
Redshift space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modeling of…
Previous work (Slepian 2024) showed that the Smith-Zaldarriaga (2011) algorithm to realize Cosmic Microwave Background (CMB) maps with any desired harmonic-space bispectrum could be generalized to produce a 3D density field with any desired…
The 3-Point Correlation Function (3PCF), which measures correlations between triplets of galaxies encodes information about peculiar velocities, which distort the observed positions of galaxies along the line of sight away from their true…
We consider the long-standing problem of predicting the hierarchical clustering amplitudes $S_p$ in the strongly non-linear regime of gravitational evolution. N-body results for the non-linear evolution of the bispectrum (the Fourier…
The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on…
The nature of dark energy and the complete theory of gravity are two central questions currently facing cosmology. A vital tool for addressing them is the 3-point correlation function (3PCF), which probes deviations from a spatially random…
We establish a practical method for the joint analysis of anisotropic galaxy two- and three-point correlation functions (2PCF and 3PCF) on the basis of the decomposition formalism of the 3PCF using tri-polar spherical harmonics. We perform…
Recent measurements of the galaxy 4-Point Correlation Function (4PCF) have seemingly detected non-zero parity-odd modes at high significance. Since gravity, the primary driver of galaxy formation and evolution is parity-even, any parity…