NON-GAUSSIAN ERROR CONTRIBUTION TO LIKELIHOOD ANALYSIS OF THE MATTER POWER SPECTRUM

We study the sample variance of the matter power spectrum for the standard Λ cold dark matter universe. We use a total of 5000 cosmological N-body simulations to study in detail the distribution of best-fit cosmological parameters and the baryon acoustic peak positions. The obtained distribution is compared with the results from the Fisher matrix analysis with and without including non-Gaussian errors. For the Fisher matrix analysis, we compute the derivatives of the matter power spectrum with respect to cosmological parameters using directly full nonlinear simulations. We show that the non-Gaussian errors increase the unmarginalized errors by up to a factor of five for kmax = 0.4 h Mpc−1 if there is only one free parameter, provided other parameters are well determined by external information. On the other hand, for multi-parameter fitting, the impact of the non-Gaussian errors is significantly mitigated due to severe parameter degeneracies in the power spectrum. The distribution of the acoustic peak positions is well described by a Gaussian distribution, with its width being consistent with the statistical interval predicted from the Fisher matrix. We also examine systematic bias in the best-fit parameter due to the non-Gaussian errors. The bias is found to be smaller than the 1σ statistical error for both the cosmological parameters and the acoustic scale positions.

[1]  S. Phleps,et al.  A new model for the full shape of the large-scale power spectrum , 2010, 1007.0755.

[2]  A. Szalay,et al.  THE BARYONIC ACOUSTIC FEATURE AND LARGE-SCALE CLUSTERING IN THE SLOAN DIGITAL SKY SURVEY LUMINOUS RED GALAXY SAMPLE , 2010 .

[3]  D. Eisenstein,et al.  HIGH-PRECISION PREDICTIONS FOR THE ACOUSTIC SCALE IN THE NONLINEAR REGIME , 2009, 0910.5005.

[4]  A. Szalay,et al.  The Baryonic Acoustic Feature and Large-Scale Clustering in the SDSS LRG Sample , 2009, 0908.2598.

[5]  M. Takada,et al.  Nonlinear power spectrum in the presence of massive neutrinos: perturbation theory approach, galaxy bias and parameter forecasts , 2009, 0907.2922.

[6]  Alexander S. Szalay,et al.  Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample , 2009, 0907.1660.

[7]  Alexander S. Szalay,et al.  Cosmological constraints from the clustering of the Sloan Digital Sky Survey DR7 luminous red galaxies (vol 404, pg 60, 2010) , 2009, 0907.1659.

[8]  P. Schneider,et al.  A fitting formula for the non-Gaussian contribution to the lensing power spectrum covariance , 2009, 0907.1524.

[9]  Masanori Sato,et al.  SIMULATIONS OF WIDE-FIELD WEAK LENSING SURVEYS. I. BASIC STATISTICS AND NON-GAUSSIAN EFFECTS , 2009, 0906.2237.

[10]  Takahiro Nishimichi,et al.  Nonlinear evolution of baryon acoustic oscillations from improved perturbation theory in real and redshift spaces , 2009, 0906.0507.

[11]  O. Dor'e,et al.  Dark energy from large-scale structure lensing information , 2009, 0905.0499.

[12]  O. Dor'e,et al.  The Non-Linear Fisher Information content of cosmic shear surveys , 2009, 0905.0501.

[13]  A. Szalay,et al.  REJUVENATING THE MATTER POWER SPECTRUM: RESTORING INFORMATION WITH A LOGARITHMIC DENSITY MAPPING , 2009, 0903.4693.

[14]  N. Yoshida,et al.  SIMULATIONS OF BARYON ACOUSTIC OSCILLATIONS. II. COVARIANCE MATRIX OF THE MATTER POWER SPECTRUM , 2009, 0902.0371.

[15]  P. Schneider,et al.  The non-Gaussianity of the cosmic shear likelihood or how odd is the Chandra Deep Field South? , 2009, 0901.3269.

[16]  Durham,et al.  Cosmological parameter constraints from SDSS luminous red galaxies: a new treatment of large-scale clustering , 2009, 0901.2570.

[17]  John Dubinski,et al.  THE HORIZON RUN N-BODY SIMULATION: BARYON ACOUSTIC OSCILLATIONS AND TOPOLOGY OF LARGE-SCALE STRUCTURE OF THE UNIVERSE , 2008, 0812.1392.

[18]  D. Higdon,et al.  THE COYOTE UNIVERSE. I. PRECISION DETERMINATION OF THE NONLINEAR MATTER POWER SPECTRUM , 2008, 0812.1052.

[19]  Ipmu,et al.  Constraints on Neutrino Masses from Weak Lensing , 2008, 0810.4921.

[20]  Tim Eifler,et al.  Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation , 2008, 0810.4254.

[21]  M. Takada,et al.  The impact of non‐Gaussian errors on weak lensing surveys , 2008, 0810.4170.

[22]  R. Smith.  Covariance of cross-correlations: towards efficient measures for large-scale structure , 2008, 0810.1960.

[23]  Y. Jing,et al.  Modeling Nonlinear Evolution of Baryon Acoustic Oscillations: Convergence Regime of $N$-body Simulations and Analytic Models , 2008, 0810.0813.

[24]  T. Kitching,et al.  Deconstructing Baryon Acoustic Oscillations: A Comparison of Methods , 2008, 0810.0003.

[25]  Kazuhiro Yamamoto,et al.  Damping of the baryon acoustic oscillations in the matter power spectrum as a probe of the growth factor , 2008, 0809.4538.

[26]  E. Gaztañaga,et al.  Clustering of luminous red galaxies – IV. Baryon acoustic peak in the line-of-sight direction and a direct measurement of H(z) , 2008, 0807.3551.

[27]  T. Matsubara.  Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture , 2008, 0807.1733.

[28]  U. Pen,et al.  Information Content in the Galaxy Angular Power Spectrum from the Sloan Digital Sky Survey and Its Implication on Weak-Lensing Analysis , 2008, 0807.1538.

[29]  R. Takahashi.  Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe , 2008, 0806.1437.

[30]  M. Pietroni,et al.  Flowing with time: a new approach to non-linear cosmological perturbations , 2008, 0806.0971.

[31]  E. Komatsu,et al.  EXTRACTING ANGULAR DIAMETER DISTANCE AND EXPANSION RATE OF THE UNIVERSE FROM TWO-DIMENSIONAL GALAXY POWER SPECTRUM AT HIGH REDSHIFTS: BARYON ACOUSTIC OSCILLATION FITTING VERSUS FULL MODELING , 2008, 0805.4238.

[32]  A. Slosar,et al.  Constraints on local primordial non-Gaussianity from large scale structure , 2008, 0805.3580.

[33]  Eiichiro Komatsu,et al.  PERTURBATION THEORY RELOADED. II. NONLINEAR BIAS, BARYON ACOUSTIC OSCILLATIONS, AND MILLENNIUM SIMULATION IN REAL SPACE , 2008, 0805.2632.

[34]  D. Eisenstein,et al.  Non-linear Structure Formation and the Acoustic Scale , 2022 .

[35]  P. Schneider,et al.  The removal of shear-ellipticity correlations from the cosmic shear signal , 2008, 0905.0393.

[36]  N. Padmanabhan,et al.  Constraining anisotropic baryon oscillations , 2008, 0804.0799.

[37]  Durham,et al.  What is the best way to measure baryonic acoustic oscillations , 2008, 0804.0233.

[38]  Edward J. Wollack,et al.  FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: COSMOLOGICAL INTERPRETATION , 2008, 0803.0547.

[39]  N. Yoshida,et al.  Simulations of baryon acoustic oscillations – I. Growth of large-scale density fluctuations , 2008, 0802.1808.

[40]  A. Szalay,et al.  Large-Scale Anisotropic Correlation Function of SDSS Luminous Red Galaxies , 2007, 0711.3640.

[41]  T. Matsubara,et al.  Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space , 2007, 0711.2521.

[42]  M. Neyrinck,et al.  Baryon oscillations in galaxy and matter power-spectrum covariance matrices , 2007, 0710.3586.

[43]  T. Hiramatsu,et al.  A Closure Theory for Nonlinear Evolution of Cosmological Power Spectra , 2007, 0708.1367.

[44]  M. Crocce,et al.  Nonlinear evolution of baryon acoustic oscillations , 2007, 0704.2783.

[45]  S. Matarrese,et al.  Resumming cosmic perturbations , 2007, astro-ph/0703563.

[46]  S. Matarrese,et al.  Baryonic Acoustic Oscillations via the Renormalization Group , 2007, astro-ph/0702653.

[47]  Durham,et al.  The detectability of baryonic acoustic oscillations in future galaxy surveys. , 2007, astro-ph/0702543.

[48]  C. V. D. Bruck,et al.  Moduli corrections to D-term inflation , 2006, hep-th/0610195.

[49]  Y. Jing,et al.  Bispectrum and Nonlinear Biasing of Galaxies: Perturbation Analysis, Numerical Simulation, and SDSS Galaxy Clustering , 2006, astro-ph/0609740.

[50]  R. Smith,et al.  Scale Dependence of Halo and Galaxy Bias: Effects in Real Space , 2006, astro-ph/0609547.

[51]  Michael S. Warren,et al.  Simulations of baryon oscillations , 2006, astro-ph/0607061.

[52]  P. Mcdonald.  Dark matter clustering: a simple renormalization group approach , 2006, astro-ph/0606028.

[53]  G. Bernstein,et al.  Systematic effects in the sound horizon scale measurements , 2006, astro-ph/0605594.

[54]  D. Eisenstein,et al.  Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak , 2006, astro-ph/0604362.

[55]  M. Neyrinck,et al.  Information content in the halo-model dark-matter power spectrum -- II. Multiple cosmological parameters , 2006, astro-ph/0610211.

[56]  E. Komatsu,et al.  Perturbation Theory Reloaded: Analytical Calculation of Nonlinearity in Baryonic Oscillations in the Real-Space Matter Power Spectrum , 2006, astro-ph/0604075.

[57]  M. Crocce,et al.  Cosmology and the Bispectrum , 2006, astro-ph/0604505.

[58]  U. Colorado,et al.  Information content of the non‐linear power spectrum: the effect of beat‐coupling to large scales , 2005, astro-ph/0511418.

[59]  N. University,et al.  On measuring the covariance matrix of the non-linear power spectrum from simulations , 2005, astro-ph/0511416.

[60]  M. Crocce,et al.  Renormalized cosmological perturbation theory , 2005, astro-ph/0509418.

[61]  D. Eisenstein,et al.  Baryonic Acoustic Oscillations in Simulated Galaxy Redshift Surveys , 2005, astro-ph/0507338.

[62]  V. Springel.  The Cosmological simulation code GADGET-2 , 2005, astro-ph/0505010.

[63]  A. Hamilton,et al.  Information content of the non-linear matter power spectrum , 2005, astro-ph/0502081.

[64]  R. Ellis,et al.  The 2dF Galaxy Redshift Survey: power-spectrum analysis of the final data set and cosmological implications , 2005, astro-ph/0501174.

[65]  R. Nichol,et al.  Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies , 2005, astro-ph/0501171.

[66]  D. Huterer,et al.  Calibrating the nonlinear matter power spectrum: Requirements for future weak lensing surveys , 2004, astro-ph/0412142.

[67]  T. Matsubara.  Correlation Function in Deep Redshift Space as a Cosmological Probe , 2004, astro-ph/0408349.

[68]  D. Eisenstein,et al.  Probing Dark Energy with Baryonic Acoustic Oscillations from Future Large Galaxy Redshift Surveys , 2003, astro-ph/0307460.

[69]  C. Blake,et al.  SUBMITTED TO THE ASTROPHYSICAL JOURNAL: MARCH 17, 2003 Preprint typeset using L ATEX style emulateapj v. 26/01/00 OVER 5000 DISTANT EARLY-TYPE GALAXIES IN COMBO-17: A RED SEQUENCE AND ITS EVOLUTION SINCE Z ∼ 1 , 2003 .

[70]  J. Peacock,et al.  Stable clustering, the halo model and non-linear cosmological power spectra , 2002, astro-ph/0207664.

[71]  A. Cooray,et al.  Power Spectrum Covariance of Weak Gravitational Lensing , 2000, astro-ph/0012087.

[72]  V. Springel,et al.  GADGET: a code for collisionless and gasdynamical cosmological simulations , 2000, astro-ph/0003162.

[73]  A. Lewis,et al.  Efficient computation of CMB anisotropies in closed FRW models , 1999, astro-ph/9911177.

[74]  M. Zaldarriaga,et al.  Power Spectrum Correlations Induced by Nonlinear Clustering , 1999, astro-ph/9901099.

[75]  J. Peacock,et al.  Baryonic signatures in Large-Scale Structure , 1998, astro-ph/9812214.

[76]  M. White,et al.  The growth of correlations in the matter power spectrum , 1998, astro-ph/9812129.

[77]  U. Seljak,et al.  A Line of sight integration approach to cosmic microwave background anisotropies , 1996, astro-ph/9603033.

[78]  Max Tegmark,et al.  Karhunen-Loève Eigenvalue Problems in Cosmology: How Should We Tackle Large Data Sets? , 1996, astro-ph/9603021.

[79]  J. Peacock,et al.  Power spectrum analysis of three-dimensional redshift surveys , 1993, astro-ph/9304022.

[80]  B. Paczyński,et al.  An evolution free test for non-zero cosmological constant , 1979, Nature.