arXiv subjects

Takahiko Matsubara

Publications and source records attributed to Takahiko Matsubara.

At least 55 records · Page 3Linked to original sources

arXiv2011

Simulations of Wide-Field Weak Lensing Surveys II: Covariance Matrix of Real Space Correlation Functions

Using 1000 ray-tracing simulations for a Λ-dominated cold dark model in Sato et al. (2009), we study the covariance matrix of cosmic shear correlation functions, which is the standard statistics used in the previous measurements. The shear correlation function of a particular separation angle is affected by Fourier modes over a wide range of multipoles, even beyond a survey area, which complicates the analysis of the covariance matrix. To overcome such obstacles we first construct Gaussian shear simulations from the 1000 realizations, and then use the Gaussian simulations to disentangle the Gaussian covariance contribution to the covariance matrix we measured from the original simulations. We found that an analytical formula of Gaussian covariance overestimates the covariance amplitudes due to an effect of finite survey area. Furthermore, the clean separation of the Gaussian covariance allows to examine the non-Gaussian covariance contributions as a function of separation angles and source redshifts. For upcoming surveys with typical source redshifts of z_s=0.6 and 1.0, the non-Gaussian contribution to the diagonal covariance components at 1 arcminute scales is greater than the Gaussian contribution by a factor of 20 and 10, respectively. Predictions based on the halo model qualitatively well reproduce the simulation results, however show a sizable disagreement in the covariance amplitudes. By combining these simulation results we develop a fitting formula to the covariance matrix for a survey with arbitrary area coverage, taking into account effects of the finiteness of survey area on the Gaussian covariance.

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arXiv2011

Nonlinear Perturbation Theory Integrated with Nonlocal Bias, Redshift-space Distortions, and Primordial Non-Gaussianity

The standard nonlinear perturbation theory of the gravitational instability is extended to incorporate the nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. We show that local Eulerian bias is not generally compatible to local Lagrangian bias in nonlinear regime. The Eulerian and Lagrangian biases are nonlocally related order by order in the general perturbation theory. The relation between Eulerian and Lagrangian kernels of density perturbations with biasing are derived. The effects of primordial non-Gaussianity and redshift-space distortions are also incorporated in our general formalism, and diagrammatic methods are introduced. Vertex resummations of higher-order perturbations in the presence of bias are considered. Resummations of Lagrangian bias are shown to be essential to handle biasing schemes in a general framework.

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arXiv2010

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 Lambda 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 5 for k_{max}=0.4h/Mpc 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 sigma statistical error for both the cosmological parameters and the acoustic scale positions.

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arXiv2010

Constraints on primordial non-Gaussianity from Galaxy-CMB lensing cross-correlation

Recent studies have shown that the primordial non-Gaussianity affects clustering of dark matter halos through a scale-dependent bias and various constraints on the non-Gaussianity through this scale-dependent bias have been placed. Here we introduce the cross-correlation between the CMB lensing potential and the galaxy angular distribution to effectively extract information about the bias from the galaxy distribution. Then, we estimate the error of non-linear parameter, f_NL, for the on-going CMB experiments and galaxy surveys, such as Planck and Hyper Suprime-Cam (HSC). We found that for the constraint on f_NL with Planck and HSC, the wide field galaxy survey is preferable to the deep one, and the expected error on f_NL can be as small as: Δf_NL ~ 20 for b_0 = 2 and Δf_NL ~ 10 for b_0 = 4, where b_0 is the linear bias parameter. It is also found that future wide field galaxy survey could achieve Δf_NL ~ 5 with CMB prior from Planck if one could observe highly biased objects at higher redshift (z ~ 2).

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arXiv2010

Analytic Minkowski Functionals of the Cosmic Microwave Background: Second-order Non-Gaussianity with Bispectrum and Trispectrum

Analytic formulas of Minkowski functionals in two-dimensional random fields are derived, including effects of second-order non-Gaussianity in the presence of both the bispectrum and trispectrum. The set of formulas provides a promising method to constrain the primordial non-Gaussianity of the universe by temperature fluctuations in the cosmic microwave background radiation. In a case of local-type non-Gaussianity, the Minkowski functionals are analytically given by powers of quadratic and cubic parameters, $f_{\rm NL}$ and $g_{\rm NL}$. Our formulas are not restricted to this particular model, and applicable to a wide class of non-Gaussian models. The analytic formulas are compared to numerical evaluations from non-Gaussian realizations of temperature maps, showing very good agreements.

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arXiv2009

Limits on Isocurvature Perturbations from Non-Gaussianity in WMAP Temperature Anisotropies

We study the effect of primordial isocurvature perturbations on non-Gaussian properties of CMB temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the Gaussian variable sigma, S=sigma^2- , can give the same signal-to-noise as f_NL=30 even if we impose the current observational limit on the fraction of isocurvature perturbations contained in the primordial power spectrum alpha. We give constraints on isocurvature non-Gaussianity from Minkowski Functionals using WMAP 5-year data. We do not find a significant signal of the isocurvature non-Gaussianity. For the quadratic isocurvature model, we obtain a stringent upper limit on the isocurvature fraction alpha<0.070 (95% CL) for a scale invariant spectrum which is comparable to the limit obtained from the power spectrum.

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arXiv2009

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

We use 5000 cosmological N-body simulations of 1(Gpc/h)^3 box for the concordance LCDM model in order to study the sampling variances of nonlinear matter power spectrum. We show that the non-Gaussian errors can be important even on large length scales relevant for baryon acoustic oscillations (BAO). Our findings are (1) the non-Gaussian errors degrade the cumulative signal-to-noise ratios (S/N) 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 WFMOS-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.

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arXiv2008

Signature of Primordial Non-Gaussianity on Matter Power Spectrum

Employing the perturbative treatment of gravitational clustering, we discuss possible effects of primordial non-Gaussianity on the matter power spectrum. As gravitational clustering develops, the coupling between different Fourier modes of density perturbations becomes important and the primordial non-Gaussianity which intrinsically possesses a non-trivial mode-correlation can affect the late-time evolution of the power spectrum. We quantitatively estimate the non-Gaussian effect on power spectrum from the perturbation theory. The potential impact on the cosmological parameter estimation using the power spectrum are investigated based on the Fisher-matrix formalism. In addition, on the basis of the local biasing prescription, non-Gaussian effects on the galaxy power spectrum are considered, showing that the scale-dependent biasing arises from a local-type primordial non-Gaussianity. On the other hand, an equilateral-type non-Gaussianity does not induce such scale-dependence because of weaker mode-correlations between small and large Fourier modes.

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arXiv2008

Modeling Nonlinear Evolution of Baryon Acoustic Oscillations: Convergence Regime of N-body Simulations and Analytic Models

We use 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 ΛCold Dark Matter universe. We compare the results of N-body simulations against three analytical model predictions; standard perturbation theory, renormalized perturbation theory, and the closure approximation. We include the effects from finite simulation box size in the comparison. We determine the values of the maximum wavenumbers, k^{lim}_{1%} and k^{lim}_{3%}, below which the analytic models and the simulation results agree to within 1 and 3 percent, respectively. We then provide a simple empirical function which describes the convergence regime determined by comparison between our simulations and the analytical models. We find that if we use the Fourier modes within the convergence regime alone, the characteristic scale of baryon acoustic oscillations can be determined within 1% accuracy from future surveys with a volume of a few h^{-3}Gpc^3 at z\sim1 or z\sim3 in the absence of any systematic distortion of the power spectrum.

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arXiv2008

Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture

The nonlinear perturbation theory of gravitational instability is extended to include effects of both biasing and redshift-space distortions, which are inevitable in predicting observable quantities in galaxy surveys. The precise determination of scales of baryon acoustic oscillations is crucial to investigate the nature of dark energy by galaxy surveys. We find that a local Lagrangian bias and redshift-space distortions are naturally incorporated in our formalism of perturbation theory with a resummation technique via the Lagrangian picture. Our formalism is applicable to any biasing scheme which is local in Lagrangian space, including the halo bias as a special case. Weakly nonlinear effects on halo clustering in redshift space are analytically given.We assume only a fundamental idea of the halo model: haloes form according to the extended Press-Schechter theory, and the spatial distributions are locally biased in Lagrangian space. There is no need for assuming the spherical collapse model to follow the dynamical evolution, which is additionally assumed in standard halo prescriptions. One-loop corrections to the power spectrum and correlation function of haloes in redshift space are explicitly derived and presented. Instead of relying on expensive numerical simulations, our approach provides an analytic way of investigating the weakly nonlinear effects, simultaneously including the nonlinear biasing and nonlinear redshift-space distortions. Nonlinearity introduces a weak scale dependence in the halo bias. The scale dependence is a smooth function in Fourier space, and the bias does not critically change the feature of baryon acoustic oscillations in the power spectrum. The same feature in the correlation function is less affected by nonlinear effects of biasing.

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arXiv2008

Limits on Primordial Non-Gaussianity from Minkowski Functionals of the WMAP Temperature Anisotropies

We present an analysis of the Minkowski Functionals (MFs) describing the WMAP three-year temperature maps to place limits on possible levels of primordial non-Gaussianity. In particular, we apply perturbative formulae for the MFs to give constraints on the usual non-linear coupling constant fNL. The theoretical predictions are found to agree with the MFs of simulated CMB maps including the full effects of radiative transfer. The agreement is also very good even when the simulation maps include various observational artifacts, including the pixel window function, beam smearing, inhomogeneous noise and the survey mask. We find accordingly that these analytical formulae can be applied directly to observational measurements of fNL without relying on non-Gaussian simulations. Considering the bin-to-bin covariance of the MFs in WMAP in a chi-square analysis, we find that the primordial non-Gaussianity parameter is constrained to lie in the range -70<fNL<91 at 95% C.L. using the Q+V+W co-added maps.

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arXiv2008

Simulations of Baryon Acoustic Oscillations I: Growth of Large-Scale Density Fluctuations

We critically examine how well the evolution of large-scale density perturbations is followed in cosmological $N$-body simulations. We first run a large volume simulation and perform a mode-by-mode analysis in three-dimensional Fourier space. We show that the growth of large-scale fluctuations significantly deviates from linear theory predictions. The deviations are caused by {\it nonlinear} coupling with a small number of modes at largest scales owing to finiteness of the simulation volume. We then develop an analytic model based on second-order perturbation theory to quantify the effect. Our model accurately reproduces the simulation results. For a single realization, the second-order effect appears typically as ``zig-zag'' patterns around the linear-theory prediction, which imprints artificial ``oscillations'' that lie on the real baryon-acoustic oscillations. Although an ensemble average of a number of realizations approaches the linear theory prediction, the dispersions of the realizations remain large even for a large simulation volume of several hundred megaparsecs on a side. For the standard $Λ$CDM model, the deviations from linear growth rate are as large as 10 percent for a simulation volume with $L = 500h^{-1}$Mpc and for a bin width in wavenumber of $Δk = 0.005h$Mpc$^{-1}$, which are comparable to the intrinsic variance of Gaussian random realizations. We find that the dispersions scales as $\propto L^{-3/2} Δk^{-1/2}$ and that the mean dispersion amplitude can be made smaller than a percent only if we use a very large volume of $L > 2h^{-1}$Gpc. The finite box size effect needs to be appropriately taken into account when interpreting results from large-scale structure simulations for future dark energy surveys using baryon acoustic oscillations.

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arXiv2008

Large-Scale Anisotropic Correlation Function of SDSS Luminous Red Galaxies

We study the large-scale anisotropic two-point correlation function using 46,760 luminous red galaxies at redshifts 0.16 -- 0.47 from the Sloan Digital Sky Survey. We measure the correlation function as a function of separations parallel and perpendicular to the line-of-sight in order to take account of anisotropy of the large-scale structure in redshift space. We find a slight signal of baryonic features in the anisotropic correlation function, i.e., a ``baryon ridge'' which corresponds to a baryon acoustic peak in the spherically averaged correlation function which has already been reported using the same sample. The baryon ridge has primarily a spherical structure with a known radius in comoving coordinates. It enables us to divide the redshift distortion effects into dynamical and geometrical components and provides further constraints on cosmological parameters, including the dark energy equation-of-state. With an assumption of a flat $Λ$ cosmology, we find the best-fit values of $Ω_{\rm m} = 0.218^{+0.047}_{-0.037}$ and $Ω_{\rm b} = 0.047^{+0.016}_{-0.016}$ (68% C.L.) when we use the overall shape of the anisotropic correlation function of $40<s<200\himpc$ including a scale of baryon acoustic oscillations. When an additional assumption $Ω_{\rm b}h^2=0.024$ is adopted, we obtain $Ω_{\rm DE}=0.770^{+0.051}_{-0.040}$ and $w=-0.93^{+0.45}_{-0.35}$. These constraints are estimated only from our data of the anisotropic correlation function, and they agree quite well with values both from the cosmic microwave background (CMB) anisotropies and from other complementary statistics using the LRG sample. With the CMB prior from the 3 year WMAP results, we give stronger constraints on those parameters.

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arXiv2008

Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space

We develop a new approach to study the nonlinear evolution in the large-scale structure of the Universe both in real space and in redshift space, extending the standard perturbation theory of gravitational instability. Infinite series of terms in standard Eulerian perturbation theory are resummed as a result of our starting from a Lagrangian description of perturbations. Delicate nonlinear effects on scales of the baryon acoustic oscillations are more accurately described by our method than the standard one. Our approach differs from other resummation techniques recently proposed, such as the renormalized perturbation theory, etc., in that we use simple techniques and thus resulting equations are undemanding to evaluate, and in that our approach is capable of quantifying the nonlinear effects in redshift space. The power spectrum and correlation function of our approach are in good agreement with numerical simulations in literature on scales of baryon acoustic oscillations. Especially, nonlinear effects on the baryon acoustic peak of the correlation function are accurately described both in real space and in redshift space. Our approach provides a unique opportunity to analytically investigate the nonlinear effects on baryon acoustic scales in observable redshift space, which is requisite in constraining the nature of dark energy, the curvature of the Universe, etc., by redshift surveys.

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arXiv2006

Effects of Smoothing Functions in Cosmological Counts-in-Cells Analysis

A method of counts-in-cells analysis of galaxy distribution is investigated with arbitrary smoothing functions in obtaining the galaxy counts. We explore the possiblity of optimizing the smoothing function, considering a series of $m$-weight Epanechnikov kernels. The popular top-hat and Gaussian smoothing functions are two special cases in this series. In this paper, we mainly consider the second moments of counts-in-cells as a first step. We analytically derive the covariance matrix among different smoothing scales of cells, taking into account possible overlaps between cells. We find that the Epanechnikov kernel of $m=1$ is better than top-hat and Gaussian smoothing functions in estimating cosmological parameters. As an example, we estimate expected parameter bounds which comes only from the analysis of second moments of galaxy distributions in a survey which is similar to the Sloan Digital Sky Survey.

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arXiv2006

Primordial Non-Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large-scale Structure

We derive analytical formulae for the Minkowski Functions of the cosmic microwave background (CMB) and large-scale structure (LSS) from primordial non-Gaussianity. These formulae enable us to estimate a non-linear coupling parameter, f_NL, directly from the CMB and LSS data without relying on numerical simulations of non-Gaussian primordial fluctuations. One can use these formulae to estimate statistical errors on f_NL from Gaussian realizations, which are much faster to generate than non-Gaussian ones, fully taking into account the cosmic/sampling variance, beam smearing, survey mask, etc. We show that the CMB data from the Wilkinson Microwave Anisotropy Probe should be sensitive to |f_NL|\simeq 40 at the 68% confidence level. The Planck data should be sensitive to |f_NL|\simeq 20. As for the LSS data, the late-time non-Gaussianity arising from gravitational instability and galaxy biasing makes it more challenging to detect primordial non-Gaussianity at low redshifts. The late-time effects obscure the primordial signals at small spatial scales. High-redshift galaxy surveys at z>2 covering \sim 10Gpc^3 volume would be required for the LSS data to detect |f_NL|\simeq 100. Minkowski Functionals are nicely complementary to the bispectrum because the Minkowski Functionals are defined in real space and the bispectrum is defined in Fourier space. This property makes the Minksowski Functionals a useful tool in the presence of real-world issues such as anisotropic noise, foreground and survey masks. Our formalism can be extended to scale-dependent f_NL easily.

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arXiv2006

Statistics of Fourier Modes in Non-Gaussian Fields

Fourier methods are fundamental tools to analyze random fields. Statistical structures of homogeneous Gaussian random fields are completely characterized by the power spectrum. In non-Gaussian random fields, polyspectra, higher-order counterparts of the power spectrum, are usually considered to characterize statistical information contained in the fields. However, it is not trivial how the Fourier modes are distributed in general non-Gaussian fields. In this paper, distribution functions of Fourier modes are directly considered and their explicit relations to the polyspectra are given. Under the condition that any of the polyspectra does not diverge, the distribution function is expanded by dimensionless combinations of polyspectra and a total volume in which the Fourier transforms are performed. The expression up to second order is generally given, and higher-order results are also derived in some cases. A concept of N-point distribution function of Fourier modes are introduced and explicitly calculated. Among them, the one-point distribution function is completely given in a closed form up to arbitrary order. As an application, statistics of Fourier phases are explored in detail. A number of aspects regarding statistical properties of phases are found. It is clarified, for the first time, how phase correlations arise in general non-Gaussian fields. Some of our analytic results are tested against numerical realizations of non-Gaussian fields, showing good agreements.

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arXiv2005

Fourier Phase Analysis of SDSS Galaxies

We present a first analysis of the clustering of SDSS galaxies using the distribution function of the sum of Fourier phases. This statistic was recently proposed by one of authors as a new method to probe phase correlations of cosmological density fields. Since the Fourier phases are statistically independent of Fourier amplitudes, the phase statistic plays a complementary role to the conventional two-point statistics of galaxy clustering. In particular, we focus on the distribution functions of phase sum over three closed wavevectors as a function of the configurations of triangle wavevectors. We find that the observed distribution functions of phase sum are in good agreement with the lowest-order approximation from perturbation theory. For direct comparison with observations, we construct mock catalogs from N-body simulations taking account of several observational effects such as the survey geometry, the redshift distortion, and the discreteness due to the limited number of data. Indeed the observed phase correlations for the galaxies in the range of absolute magnitude -22<Mr<-18 agree well with those for Lambda CDM predictions with sigma8=0.9 evolved from Gaussian initial condition. This agreement implies that the galaxy biasing is approximately linear in redshift space. Instead, assuming that the galaxy biasing is described by a quadratic deterministic function at scale larger than 30Mpc/h, we can constrain the ratio of the quadratic biasing parameter b2 to the linear biasing parameter b1. We find that resulting b2/b1 is mainly dependent on sigma8 and that it is well fitted by b2/b1=0.54(+-0.06)-0.62(+-0.08)sigma8 in CDM models. Indeed, b2/b1 is nearly zero when sigma8=0.9.

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