Ryuichi Takahashi

Revising the Halofit Model for the Nonlinear Matter Power Spectrum

Based on a suite of state-of-the-art high-resolution N-body simulations, we revisit the so-called halofit model as an accurate fitting formula for the nonlinear matter power spectrum. While the halofit model has frequently been used as a standard cosmological tool to predict the nonlinear matter power spectrum in a universe dominated by cold dark matter, its precision has been limited by the low resolution of N-body simulations used to determine the fitting parameters, suggesting the necessity of an improved fitting formula at small scales for future cosmological studies. We run high-resolution N-body simulations for 16 cosmological models around the Wilkinson Microwave Anisotropy Probe best-fit cosmological parameters (one-, three-, five-, and seven-year results), including dark energy models with a constant equation of state. The simulation results are used to re-calibrate the fitting parameters of the halofit model so as to reproduce small-scale power spectra of the N-body simulations, while keeping the precision at large scales. The revised fitting formula provides an accurate prediction of the nonlinear matter power spectrum in a wide range of wavenumbers (k ? 30 h?Mpc?1) at redshifts 0 ? z ? 10, with 5% precision for k ? 1 h?Mpc?1 at 0 ? z ? 10 and 10% for 1 ? k ? 10 h?Mpc?1 at 0 ? z ? 3. We discuss the impact of the improved halofit model on weak-lensing power spectra and correlation functions, and show that the improved model better reproduces ray-tracing simulation results.

Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum

We use 5000 cosmological N-body simulations of 1 h –3 Gpc3 box for the concordance ΛCDM model in order to study the sampling variances of a nonlinear matter power spectrum. We show that the non-Gaussian errors can be important even on large length scales relevant for baryon acoustic oscillations (BAOs). Our findings are the following: (1) the non-Gaussian errors degrade the cumulative signal-to-noise ratios (S/Ns) for the power spectrum amplitude by up to a factor of 2 and 4 for redshifts z = 1 and 0, respectively; (2) there is little information on the power spectrum amplitudes in the quasi-nonlinear regime, confirming the previous results; (3) the distribution of power spectrum estimators at BAO scales, among the realizations, is well approximated by a Gaussian distribution with variance that is given by the diagonal covariance component. (4) For the redshift-space power spectrum, the degradation in S/N by non-Gaussian errors is mitigated due to nonlinear redshift distortions; (5) for an actual galaxy survey, the additional shot noise contamination compromises the cosmological information inherent in the galaxy power spectrum, but also mitigates the impact of non-Gaussian errors. The S/N is degraded by up to 30% for a Wide-Field Fiber-Fed Optical Multi-Object Spectrograph-type survey; (6) the finite survey volume causes additional non-Gaussian errors via the correlations of long-wavelength fluctuations with the fluctuations we want to measure, further degrading the S/N values by about 30% even at high redshift z = 3.

PROBABILITY DISTRIBUTION FUNCTIONS OF COSMOLOGICAL LENSING: CONVERGENCE, SHEAR, AND MAGNIFICATION

We perform high resolution ray-tracing simulations to investigate probability distribution functions (PDFs) of lensing convergence, shear, and magnification on distant sources up to the redshift of zs = 20. We pay particular attention to the shot noise effect in N-body simulations by explicitly showing how it affects the variance of the convergence. We show that the convergence and magnification PDFs are closely related with each other via the approximate relation µ = (1−�) 2 , which can reproduce the behavior of PDFs surprisingly well up to the high magnification tail. The mean convergence measured in the source plane is found to be systematically negative, rather than zero as often assumed, and is correlated with the convergence variance. We provide simple analytical formulae for the PDFs, which reproduce simulated PDFs reasonably well for a wide range of redshifts and smoothing sizes. As explicit applications of our ray-tracing simulations, we examine the strong lensing probability and the magnification effects on the luminosity functions of distant galaxies and quasars. Subject headings: cosmology: theory – gravitational lensing – large-scale structure of universe – methods: N-body simulations

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 ? 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 k max = 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 1? statistical error for both the cosmological parameters and the acoustic scale positions.

Modeling Nonlinear Evolution of Baryon Acoustic Oscillations: Convergence Regime of

We used a series of cosmological N-body simulations and various analytic models to study the evolution of the matter power spectrum in real space in a A cold dark matter universe. We compared the results of N-body simulations against three analytical model predictions; standard perturbation theory, renormalized perturbation theory, and a closure approximation. We included the effects from a finite simulation box size under comparison. We determined the values of the maximum wavenumbers, k(1%)(lim) and k(3%)(lim) below which the analytic models and the simulation results agree with accuracy to within 1 and 3 percent. We then provided a simple empirical function that describes the convergence regime determined by comparisons between our simulations and the analytical models. We found that if we use the Fourier modes within the convergence regime alone. the characteristic scale of baryon acoustic oscillations can be determined with an accuracy of 1% from future surveys with a volume of a few h(-3) Gpc(3) at z similar to 1 or z similar to 3 in the absence of any systematic distortion of the power spectrum.

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We measure the redshift-space correlation function from a spectroscopic sample of 2783 emission line galaxies from the FastSound survey. The survey, which uses the Subaru Telescope and covers the redshift ranges of

-body Simulations and Analytic Models

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The Subaru FMOS galaxy redshift survey (FastSound). IV. New constraint on gravity theory from redshift space distortions at z ∼ 1.4

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Bias-Hardened CMB Lensing

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Search for a stochastic background of 100-MHz gravitational waves with laser interferometers

, is the first cosmological study at such high redshifts. We detect clear anisotropy due to redshift-space distortions (RSD) both in the correlation function as a function of separations parallel and perpendicular to the line of sight and its quadrupole moment. RSD has been extensively used to test general relativity on cosmological scales at