Large-separation expansion of peak clustering in Gaussian random fields

In the peaks approach, the formation sites of observable structures in the Universe are identified as peaks in the matter density field. The statistical properties of the clustering of peaks are particularly important in this respect. In this paper, we investigate the large-separation expansion of the correlation function of peaks in Gaussian random fields. The analytic formula up to third order is derived, and the resultant expression can be evaluated by a combination of one-dimensional fast Fourier transforms, which are evaluated very fast. The analytic formula obtained perturbatively in the large-separation limit is compared with a method of Monte-Carlo integrations, and a complementarity between the two methods is demonstrated.

[1]  C. Pichon,et al.  On the connectivity of the cosmic web: theory and implications for cosmology and galaxy formation , 2018, Monthly Notices of the Royal Astronomical Society.

[2]  F. Schmidt,et al.  Tidal shear and the consistency of microscopic Lagrangian halo approaches , 2017, 1711.06745.

[3]  F. Schmidt,et al.  Large-Scale Galaxy Bias , 2016, 1611.09787.

[4]  J. Blazek,et al.  FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory , 2016, 1609.05978.

[5]  Olga Smirnova,et al.  Nature in London , 2016 .

[6]  M. Schmittfull,et al.  Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals , 2016, 1609.00349.

[7]  M. Schmittfull,et al.  Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms , 2016 .

[8]  T. Matsubara,et al.  Impacts of biasing schemes in the one-loop integrated perturbation theory , 2016, 1604.06579.

[9]  J. Blazek,et al.  FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory , 2016, 1603.04826.

[10]  Kwan Chuen Chan,et al.  Squeezing the halo bispectrum: a test of bias models , 2015, 1512.06084.

[11]  M. Musso,et al.  Lagrangian bias of generic large-scale structure tracers , 2015, 1512.05283.

[12]  C. Pichon,et al.  Peak exclusion, stochasticity and convergence of perturbative bias expansions in 1+1 gravity , 2015, 1510.09204.

[13]  T. Eifler,et al.  The impact of intrinsic alignment on current and future cosmic shear surveys , 2015, 1506.08730.

[14]  V. Desjacques,et al.  Velocity bias in the distribution of dark matter halos , 2014, 1405.5885.

[15]  Kwan Chuen Chan,et al.  Measuring non-local Lagrangian peak bias , 2013, 1310.1401.

[16]  R. Smith,et al.  Halo stochasticity from exclusion and nonlinear clustering , 2013, 1305.2917.

[17]  T. Matsubara.  Integrated Perturbation Theory and One-loop Power Spectra of Biased Tracers , 2013, 1304.4226.

[18]  V. Desjacques.  Local bias approach to the clustering of discrete density peaks , 2012, 1211.4128.

[19]  R. Sheth,et al.  Excursion set peaks: a self-consistent model of dark halo abundances and clustering , 2012, 1210.1483.

[20]  R. Sheth,et al.  Peaks theory and the excursion set approach , 2012, 1206.3506.

[21]  T. Matsubara.  Deriving an Accurate Formula of Scale-dependent Bias with Primordial Non-Gaussianity: An Application of the Integrated Perturbation Theory , 2012, 1206.0562.

[22]  C. Pichon,et al.  Non-Gaussian statistics of critical sets in 2D and 3D: Peaks, voids, saddles, genus, and skeleton , 2011, 1110.0261.

[23]  A. Ludlow,et al.  The formation of CDM haloes – I. Collapse thresholds and the ellipsoidal collapse model , 2011, 1107.5808.

[24]  J. Lesgourgues,et al.  The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes , 2011, 1104.2933.

[25]  T. Matsubara.  Nonlinear Perturbation Theory Integrated with Nonlocal Bias, Redshift-space Distortions, and Primordial Non-Gaussianity , 2011, 1102.4619.

[26]  A. Ludlow,et al.  The peaks formalism and the formation of cold dark matter haloes , 2010, 1011.2493.

[27]  M. Crocce,et al.  Modeling Scale-Dependent Bias on the Baryonic Acoustic Scale with the Statistics of Peaks of Gaussian Random Fields , 2010, 1009.3449.

[28]  D. Pogosyan,et al.  Erratum: Invariant joint distribution of a stationary random field and its derivatives: Euler characteristic and critical point counts in 2 and 3D [Phys. Rev. DPRVDAQ1550-7998 80, 081301 (2009)] , 2010 .

[29]  C. Pichon,et al.  Invariant joint distribution of a stationary random field and its derivatives: Euler characteristic and critical point counts in 2 and 3D , 2009, 0907.1437.

[30]  F. Bernardeau,et al.  Multipoint propagators in cosmological gravitational instability , 2008, 0806.2334.

[31]  V. Desjacques.  Baryon acoustic signature in the clustering of density maxima , 2008, 0806.0007.

[32]  A. Hamilton.  Uncorrelated modes of the non-linear power spectrum , 1999, astro-ph/9905191.

[33]  J. Bond,et al.  How filaments of galaxies are woven into the cosmic web , 1995, Nature.

[34]  T. Matsubara.  Diagrammatic Methods in Statistics and Biasing in the Large-scale Structure of the Universe , 1995, astro-ph/9501056.

[35]  A. Szalay,et al.  Density and velocity correlations of peaks from random Gaussian fluctuations , 1995 .

[36]  T. Matsubara,et al.  Origin of cluster-cluster correlation functions in biased structure formation scenarios , 1994 .

[37]  P. Coles.  Galaxy formation with a local bias , 1993 .

[38]  J. Peacock,et al.  Erratum - the Clustering of Peaks in a Random Gaussian Field , 1989 .

[39]  P. Coles.  The clustering of local maxima in random noise , 1989 .

[40]  A. Szalay.  Constraints on the biasing of density fluctuations , 1988 .

[41]  Catelan,et al.  Peak number density of non-Gaussian random fields. , 1988, Physical review letters.

[42]  G. Efstathiou,et al.  The formation of dark halos in a universe dominated by cold dark matter , 1988 .

[43]  S. Rey,et al.  Correlations of peaks of Gaussian random fields , 1987 .

[44]  A. Szalay,et al.  The statistics of peaks of Gaussian random fields , 1986 .

[45]  Wise,et al.  Two-point correlation for rich clusters of galaxies. , 1986, Physical review letters.

[46]  J. Peacock,et al.  The statistics of maxima in primordial density perturbations , 1985 .

[47]  H. Politzer,et al.  Relations Between Spatial Correlations of Rich Clusters of Galaxies , 1984 .

[48]  N. Kaiser.  On the spatial correlations of Abell clusters , 1984 .

[49]  S. Rice.  Mathematical analysis of random noise , 1944 .

[50]  M. Kac.  A correction to “On the average number of real roots of a random algebraic equation” , 1943 .

[51]  B. Jones,et al.  The mass function in biased galaxy formation scenarios , 1990 .