Non-Gaussian Minkowski functionals and extrema counts in redshift space

In the context of upcoming large-scale structure surveys such as Euclid, it is of prime importance to quantify the effect of peculiar velocities on geometric probes. Hence the formalism to compute in redshift space the geometrical and topological one-point statistics of mildly non-Gaussian 2D and 3D cosmic fields is developed. Leveraging the partial isotropy of the target statistics, the Gram-Charlier expansion of the joint probability distribution of the field and its derivatives is reformulated in terms of the corresponding anisotropic variables. In particular, the cosmic non-linear evolution of the Minkowski functionals, together with the statistics of extrema are investigated in turn for 3D catalogues and 2D slabs. The amplitude of the non-Gaussian redshift distortion correction is estimated for these geometric probes. In 3D, gravitational perturbation theory is implemented in redshift space to predict the cosmic evolution of all relevant Gram-Charlier coefficients. Applications to the estimation of the cosmic parameters sigma(z) and beta=f/b1 from upcoming surveys is discussed. Such statistics are of interest for anisotropic fields beyond cosmology.

[1]  S. Prunet,et al.  Polarization transfer in relativistic magnetized plasmas , 2012, 1211.7352.

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

[3]  C. Pichon,et al.  Non-Gaussian extrema counts for CMB maps , 2011, 1107.1863.

[4]  Antonio Padilla,et al.  Modified Gravity and Cosmology , 2011, 1106.2476.

[5]  F. Bernardeau,et al.  Cosmological large-scale structures beyond linear theory in modified gravity , 2011, 1102.1907.

[6]  Changbom Park,et al.  TOPOLOGY OF A LARGE-SCALE STRUCTURE AS A TEST OF MODIFIED GRAVITY , 2010, 1010.3035.

[7]  S. Saito,et al.  Baryon Acoustic Oscillations in 2D: Modeling Redshift-space Power Spectrum from Perturbation Theory , 2010, 1006.0699.

[8]  J. Gott,et al.  Using the topology of large-scale structure to constrain dark energy , 2010, 1005.3631.

[9]  T. Matsubara.  Analytic Minkowski Functionals of the Cosmic Microwave Background: Second-order Non-Gaussianity with Bispectrum and Trispectrum , 2010, 1001.2321.

[10]  K. Koyama,et al.  Scale dependence of halo bispectrum from non-Gaussian initial conditions in cosmological N-body simulations , 2009, 0911.4768.

[11]  R. Sheth,et al.  Redshift space correlations and scale-dependent stochastic biasing of density peaks , 2009, 0909.4544.

[12]  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.

[13]  J. Cardoso,et al.  The local theory of the cosmic skeleton , 2008, 0811.1530.

[14]  Simon Prunet,et al.  Full-sky weak-lensing simulation with 70 billion particles , 2008, 0807.3651.

[15]  F. Castander,et al.  Clustering of luminous red galaxies – III. Baryon acoustic peak in the three-point correlation , 2008 .

[16]  Alexander S. Szalay,et al.  Measuring the Baryon Acoustic Oscillation scale using the Sloan Digital Sky Survey and 2dF Galaxy Redshift Survey , 2007 .

[17]  Korea,et al.  Genus topology of the cosmic microwave background from the WMAP 3-year data , 2006, astro-ph/0610764.

[18]  Changbom Park,et al.  Topology Analysis of the Sloan Digital Sky Survey. I. Scale and Luminosity Dependence , 2005, astro-ph/0507059.

[19]  R. Scoccimarro.  Redshift-space distortions, pairwise velocities and nonlinearities , 2004, astro-ph/0407214.

[20]  J. Gott,et al.  Minkowski Functionals of SDSS Galaxies I : Analysis of Excursion Sets , 2003, astro-ph/0304455.

[21]  Edward J. Wollack,et al.  First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters , 2003, astro-ph/0302209.

[22]  J. Brinkmann,et al.  Three-Dimensional Genus Statistics of Galaxies in the SDSS Early Data Release , 2002, astro-ph/0207377.

[23]  S. Colombi,et al.  Large scale structure of the universe and cosmological perturbation theory , 2001, astro-ph/0112551.

[24]  R. Teyssier.  c ○ ESO 2002 Astronomy Astrophysics , 2002 .

[25]  S. Colombi,et al.  Tree structure of a percolating Universe. , 2000, Physical review letters.

[26]  T. Matsubara.  Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory , 2000, astro-ph/0006269.

[27]  N. Seto.  Perturbative Analysis of Adaptive Smoothing Methods in Quantifying Large-Scale Structure , 2000, astro-ph/0002315.

[28]  A. Lazarian,et al.  Velocity Modification of H I Power Spectrum , 1999, astro-ph/9901241.

[29]  Joshua A. Frieman,et al.  The Bispectrum as a Signature of Gravitational Instability in Redshift Space , 1998, astro-ph/9808305.

[30]  L. Moscardini,et al.  Large-scale bias in the Universe - II. Redshift-space bispectrum , 1998, Monthly Notices of the Royal Astronomical Society.

[31]  S. Blinnikov,et al.  Expansions for nearly Gaussian distributions , 1997 .

[32]  J. Frieman,et al.  Nonlinear Evolution of the Bispectrum of Cosmological Perturbations , 1997, astro-ph/9704075.

[33]  L. Amendola.  Non-Gaussian likelihood function and COBE data , 1996 .

[34]  T. Matsubara.  Statistics of Isodensity Contours in Redshift Space , 1995, astro-ph/9501055.

[35]  T. Matsubara.  Analytic Expression of the Genus in a Weakly Non-Gaussian Field Induced by Gravity , 1994, astro-ph/9405037.

[36]  F. Bernardeau,et al.  Properties of the Cosmological Density Distribution Function , 1994, astro-ph/9403028.

[37]  D. Weinberg,et al.  Weakly Non-Linear Gaussian Fluctuations and the Edgeworth Expansion , 1993, astro-ph/9308012.

[38]  R. Scaramella,et al.  Non-Gaussian temperature fluctuations in the cosmic microwave background sky from a random Gaussian density field , 1991 .

[39]  A. Kashlinsky,et al.  Large-scale structure in the Universe , 1991, Nature.

[40]  Changbom Park,et al.  Topology of microwave background fluctuations - Theory , 1990 .

[41]  D. Weinberg,et al.  Topology of large-scale structure. IV - Topology in two dimensions , 1989 .

[42]  D. Weinberg,et al.  The area of isodensity contours in cosmological models and galaxy surveys , 1989 .

[43]  D. Weinberg,et al.  The topology of large-scale structure. III: Analysis of observations , 1989 .

[44]  J. Gott.  I. MEASURING THE TOPOLOGY OF LARGE-SCALE STRUCTURE IN THE UNIVERSE , 1988 .

[45]  P. Coles.  Statistical geometry and the microwave background , 1988 .

[46]  B. Ryden.  The area of isodensity contours as a measure of large-scale structure , 1988 .

[47]  D. Weinberg,et al.  The topology of large-scale structure. II - Nonlinear evolution of Gaussian models , 1988 .

[48]  D. Weinberg,et al.  The topology of large-scale structure. I - Topology and the random phase hypothesis , 1987 .

[49]  J. Richard Gott,et al.  A quantitative approach to the topology of large-scale structure , 1987 .

[50]  N. Kaiser.  Clustering in real space and in redshift space , 1987 .

[51]  J. R. Bond,et al.  The statistics of cosmic background radiation fluctuations , 1987 .

[52]  D. Weinberg,et al.  The topology of the large-scale structure of the universe , 1986 .

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

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

[55]  R. Adler,et al.  The Geometry of Random Fields , 1982 .

[56]  J. Huchra,et al.  Groups of galaxies. I. Nearby groups , 1982 .

[57]  E. Turner,et al.  A statistical method for determining the cosmological density parameter from the redshifts of a complete sample of galaxies. , 1977 .

[58]  B. Warner,et al.  Observations of Rapid Blue Variables–III HL TAU-76 , 1972 .

[59]  J. C. Jackson.  A Critique of Rees's Theory of Primordial Gravitational Radiation , 1972 .

[60]  J. Chambers,et al.  On methods of asymptotic approximation for multivariate distributions. , 1967, Biometrika.

[61]  Maurice G. Kendall,et al.  The advanced theory of statistics , 1945 .

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

[63]  Jürgen Jost,et al.  Riemannian Geometry and Geometric Analysis, 5th Edition , 2008 .

[64]  Julius Wess,et al.  The geometry of a , 1999 .

[65]  H. Hadwiger.  Vorlesungen über Inhalt, Oberfläche und Isoperimetrie , 1957 .