Takahiko Matsubara

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 corresponding 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 ? cosmology, we find the best-fit values of -->?m = 0.218?0.037+0.047 and -->?b = 0.047 ? 0.016 (68% CL) when we use the overall shape of the anisotropic correlation function of -->40 h?1 Mpc including a scale of baryon acoustic oscillations. When an additional assumption of -->?bh2 = 0.024 is adopted, we obtain -->?DE = 0.770?0.040+0.051 and -->w = ? 0.93?0.35+0.45. 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.

Correlation Function in Deep Redshift Space as a Cosmological Probe

Recent developments in galaxy surveys enable us to investigate the deep, high-redshift, universe. We quantitatively present the physical information extractable from the observable correlation function in deep redshift space in a framework of linear theory. The correlation function depends on the underlying power spectrum, velocity distortions, and the Alcock-Paczy?ski (AP) effect. The underlying power spectrum is sensitive to the constituents of matter in the universe, the velocity distortions are sensitive to the galaxy bias as well as the amount of total matter, and the Alcock-Paczy?ski effect is sensitive to the dark energy components. Measuring the dark energy by means of the baryonic feature in the correlation function is one of the most interesting applications. We show that the baryon ridge in the correlation function serves as a statistically circular object in the AP effect. In order to sufficiently constrain the dark energy components, the redshift range of the galaxy survey should be as broad as possible. The survey area on the sky should be smaller at deep redshifts than at shallow redshifts to keep the number density as dense as possible. We illustrate an optimal survey design that is useful in cosmology. Assuming future redshift surveys of z 3, which are within the reach of present-day technology, achievable error bounds on cosmological parameters are estimated by calculating the Fisher matrix. According to an illustrated design, the equation of state of dark energy can be constrained within ?5% error assuming that the bias is unknown and marginalized over. Even when all the other cosmological parameters should be simultaneously determined, the error bound for the equation of state is up to ?10%.

Cosmological Redshift Distortion of Correlation Functions as a Probe of the Density Parameter and the Cosmological Constant

We propose cosmological redshift-space distortion of correlation functions of galaxies and quasars as a probe of both the density parameter Ω0 and the cosmological constant λ0. In particular, we show that redshift-space distortion of quasar correlation functions at z ~ 2 can in principle set a constraint on the value of λ0. This is in contrast to the popular analysis of galaxy correlation functions in redshift space which basically determines Ω0.60/b, where b is the bias parameter, but is insensitive to λ0. For specific applications, we present redshift-space distortion of correlation functions both in cold dark matter models and in power-law correlation function models, and discuss the extent to which one can discriminate between the different λ0 models.

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.

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

We present an analysis of the Minkowski Functionals (MFs) describing the Wilkinson Microwave Anisotropy Probe (WMAP) 3-yr 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 cosmic microwave background (CMB) maps including the full effects of radiative transfer. The agreement is also very good even when the simulation maps include various observational artefacts, including the pixel window function, beam smearing, inhomogeneous noise and the survey mask. We accordingly find 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 [95 per cent confidence level (C.L.)] using the Q + V + W co-added maps.

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 functionals of the cosmic microwave background (CMB) and large-scale structure (LSS) from primordial non-Gaussianity. These formulae enable us to estimate a nonlinear coupling parameter, fNL, 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 fNL 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 |fNL| 40 at the 68% confidence level. The Planck data should be sensitive to |fNL| 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 ~10 Gpc3 volume would be required for the LSS data to detect |fNL| 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 Minkowski functionals a useful tool in the presence of real-world issues such as anisotropic noise, foreground, and survey masks. Our formalism can be easily extended to scale-dependent fNL.

Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory

We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields, and provide useful formulas in application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara (1994) who derived a weakly nonlinear formula of the genus statistic in a 3D density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including 3D density field, 3D velocity field, 2D projected density field, and so forth. The results are detailed for second order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume-fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still slight meat-ball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in genus curve is proposed. Subject headings: cosmology: theory — large-scale structure of universe — methods: statistical

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 with local Lagrangian bias in the 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 is 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.

Signature of primordial non-Gaussianity on the 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 nontrivial mode correlation can affect the late-time evolution of the power spectrum. We quantitatively estimate the non-Gaussian effect on the 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.

Redshift-Space Distortions of the Correlation Function in Wide-Angle Galaxy Surveys

Using a novel two-dimensional coordinate system, we have derived a particularly simple way to express the redshift distortions in galaxy redshift surveys with arbitrary geometry in closed form. This method provides an almost ideal way to measure the value of β=Ω0.60/b in wide area surveys, since all pairs in the survey can be used for the analysis. In the limit of small angles, this result straightforwardly reduces to the plane-parallel approximation. This expansion can also be used together with more sophisticated methods such as the calculation of Karhunen-Loeve eigenvectors in redshift space for an arbitrary survey geometry. Therefore, these results should provide more precise methods in which to measure the large-scale power spectrum and the value of β simultaneously.