arXiv subjects

Naonori S. Sugiyama

Publications and source records attributed to Naonori S. Sugiyama.

At least 19 recordsLinked to original sources

arXiv2023

Triumvirate: A Python/C++ package for three-point clustering measurements

Triumvirate is a Python/C++ package for measuring the three-point clustering statistics in large-scale structure (LSS) cosmological analyses. Given a catalogue of discrete particles (such as galaxies) with their spatial coordinates, it computes estimators of the multipoles of the three-point correlation function, also known as the bispectrum in Fourier space, in the tri-polar spherical harmonic (TripoSH) decomposition proposed by Sugiyama et al. (2019). The objective of Triumvirate is to provide efficient end-to-end measurement of clustering statistics which can be fed into downstream galaxy survey analyses to constrain and test cosmological models. To this end, it builds upon the original algorithms in the hitomi code developed by Sugiyama et al. (2018, 2019), and supplies a user-friendly interface with flexible input/output (I/O) of catalogue data and measurement results, with the built program configurable through external parameter files and tracked through enhanced logging and warning/exception handling. For completeness and complementarity, methods for measuring two-point clustering statistics are also included in the package.

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arXiv2023

First test of the consistency relation for the large-scale structure using the anisotropic three-point correlation function of BOSS DR12 galaxies (An explanatory video is available at https://youtu.be/Zi36ooLPhss.)

We present, for the first time, an observational test of the consistency relation for the large-scale structure (LSS) of the Universe through a joint analysis of the anisotropic two- and three-point correlation functions (2PCF and 3PCF) of galaxies. We parameterise the breakdown of the LSS consistency relation in the squeezed limit by $E_{\rm s}$, which represents the ratio of the coefficients of the shift terms in the second-order density and velocity fluctuations. $E_{\rm s}\neq1$ is a sufficient condition under which the LSS consistency relation is violated. A novel aspect of this work is that we constrain $E_{\rm s}$ by obtaining information about the nonlinear velocity field from the quadrupole component of the 3PCF without taking the squeezed limit. Using the galaxy catalogues in the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, we obtain $E_{\rm s} = -0.92_{-3.26}^{+3.13}$, indicating that there is no violation of the LSS consistency relation in our analysis within the statistical errors. Our parameterisation is general enough that our constraint can be applied to a wide range of theories, such as multicomponent fluids, modified gravity theories, and their associated galaxy bias effects. Our analysis opens a new observational window to test the fundamental physics using the anisotropic higher-order correlation functions of galaxy clustering.

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arXiv2023

New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies

We report a new test of modified gravity theories using the large-scale structure of the Universe. This paper is the first attempt to (1) apply a joint analysis of the anisotropic components of galaxy two- and three-point correlation functions (2 and 3PCFs) to actual galaxy data and (2) constrain the nonlinear effects of degenerate higher-order scalar-tensor (DHOST) theories on cosmological scales. Applying this analysis to the Baryon Oscillation Spectroscopic Survey (BOSS) data release 12, we obtain the lower bounds of $-1.655 < ξ_{\rm t}$ and $-0.504 < ξ_{\rm s}$ at the $95\%$ confidence level on the parameters characterising the time evolution of the tidal and shift terms of the second-order velocity field. These constraints are consistent with GR predictions of $ξ_{\rm t}=15/1144$ and $ξ_{\rm s}=0$. Moreover, they represent a $35$-fold and $20$-fold improvement, respectively, over the joint analysis with only the isotropic 3PCF. We ensure the validity of our results by investigating various quantities, including theoretical models of the 3PCF, window function corrections, cumulative ${\rm S/N}$, Fisher matrices, and statistical scattering effects of mock simulation data. We also find statistically significant discrepancies between the BOSS data and the Patchy mocks for the 3PCF measurement. Finally, we package all of our 3PCF analysis codes under the name \textsc{HITOMI} and make them publicly available so that readers can reproduce all the results of this paper and easily apply them to ongoing future galaxy surveys.

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arXiv2022

Second-order peculiar velocity field as a novel probe of scalar-tensor theories

We investigate the galaxy bispectrum induced by the nonlinear gravitational evolution as a possible probe to constrain degenerate higher-order scalar tensor (DHOST) theories. We find that the signal obtained from the leading kernel of second-order density fluctuations is partially hidden by the uncertainty in the nonlinear galaxy bias, and that the kernel of second-order velocity fields instead provides unbiased information on the modification of gravity theory. Based on this fact, we propose new phenomenological time-dependent functions, written as a combination of the coefficients of the second-order kernels, which is expected to trace the higher-order growth history. We then present approximate expressions for these variables in terms of parameters that characterize the DHOST theories. We also show that the resultant formulae provides new constraints on the parameter space of the DHOST theories.

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arXiv2021

Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues

We establish a practical method for the joint analysis of anisotropic galaxy two- and three-point correlation functions (2PCF and 3PCF) on the basis of the decomposition formalism of the 3PCF using tri-polar spherical harmonics. We perform such an analysis with MultiDark Patchy mock catalogues to demonstrate and understand the benefit of the anisotropic 3PCF. We focus on scales above $80 h^{-1}\,{\rm Mpc}$, and use information from the shape and the baryon acoustic oscillation (BAO) signals of the 2PCF and 3PCF. We also apply density field reconstruction to increase the signal-noise ratio of BAO in the 2PCF measurement, but not in the 3PCF measurement. In particular, we study in detail the constraints on the angular diameter distance and the Hubble parameter. We build a model of the bispectrum or 3PCF that includes the nonlinear damping of the BAO signal in redshift space. We carefully account for various uncertainties in our analysis including theoretical models of the 3PCF, window function corrections, biases in estimated parameters from the fiducial values, the number of mock realizations to estimate the covariance matrix, and bin size. The joint analysis of the 2PCF and 3PCF monopole and quadrupole components shows a $30\%$ a nd $20\%$ improvement in Hubble parameter constraints before and after reconstruction of the 2PCF measurements, respectively, compared to the 2PCF analysis alone. This study clearly shows that the anisotropic 3PCF increases cosmological information from galaxy surveys and encourages further development of the modeling of the 3PCF on smaller scales than we consider.

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arXiv2021

Constraining Primordial Non-Gaussianity with Post-reconstructed Galaxy Bispectrum in Redshift Space

Galaxy bispectrum is a promising probe of inflationary physics in the early universe as a measure of primordial non-Gaussianity (PNG), whereas its signal-to-noise ratio is significantly affected by the mode coupling due to non-linear gravitational growth. In this paper, we examine the standard reconstruction method of linear cosmic mass density fields from non-linear galaxy density fields to de-correlate the covariance in redshift-space galaxy bispectra. In particular, we evaluate the covariance of the bispectrum for massive-galaxy-sized dark matter halos with reconstruction by using 4000 independent $N$-body simulations. Our results show that the bispectrum covariance for the post-reconstructed field approaches the Gaussian prediction at scale of $k<0.2\, h\, {\rm Mpc}^{-1}$. We also verify the leading-order PNG-induced bispectrum is not affected by details of the reconstruction with perturbative theory. We then demonstrate the constraining power of the post-reconstructed bispectrum for PNG at redshift of $\sim0.5$. Further, we perform a Fisher analysis to make a forecast of PNG constraints by galaxy bispectra including anisotropic signals. Assuming a massive galaxy sample in the SDSS Baryon Oscillation Spectroscopic Survey, we find that the post-reconstructed bispectrum can constrain the local-, equilateral- and orthogonal-types of PNG with $Δf_{\rm NL} \sim$13, 90 and 42, respectively, improving the constraints with the pre-reconstructed bispectrum by a factor of $1.3-3.2$. In conclusion, the reconstruction plays an essential role in constraining various types of PNG signatures with a level of $Δf_{\rm NL}<1$ from the galaxy bispectrum based on upcoming galaxy surveys.

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arXiv2020

Minimum variance estimation of galaxy power spectrum in redshift space

We study an efficient way to enhance the measurability of the galaxy density and/or velocity power spectrum in redshift space. It is based on the angular decomposition with the Tripolar spherical harmonic (TripoSH) basis and applicable even to galaxy distributions in wide-angle galaxy surveys. While nontrivial multipole-mode mixings are inevitable in the covariance of the Legendre decomposition coefficient commonly used in the small-angle power spectrum analysis, our analytic computation of the covariance of the TripoSH decomposition coefficient shows that such mixings are absent by virtue of high separability of the TripoSH basis, yielding the minimum variance. Via the simple signal-to-noise ratio assessment, we confirm that the detectability improvement by the TripoSH decomposition approach becomes more significant at higher multipole modes, and, e.g., the hexadecapole of the density power spectrum has two orders of magnitude improvement. The TripoSH decomposition approach is expected to be applied to not only currently available survey data but also forthcoming wide-angle one, and to bring about something new or much more accurate cosmological information.

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arXiv2020

Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the auto-covariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order perturbation theory works because the shot-noise corrections for the Patchy mocks are more dominant than other higher-order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

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arXiv2019

A complete FFT-based decomposition formalism for the redshift-space bispectrum

To fully extract cosmological information from nonlinear galaxy distribution in redshift space, it is essential to include higher-order statistics beyond the two-point correlation function. In this paper, we propose a new decomposition formalism for computing the anisotropic bispectrum in redshift space and for measuring it from galaxy samples. Our formalism uses tri-polar spherical harmonic decomposition with zero total angular momentum to compress the 3D modes distribution in the redshift-space bispectrum. This approach preserves three fundamental properties of the Universe: statistical homogeneity, isotropy, and parity-symmetry, allowing us to efficiently separate the anisotropic signal induced by redshift-space distortions (RSDs) and the Alcock-Paczyński (AP) effect from the isotropic bispectrum. The relevant expansion coefficients in terms of the anisotropic signal are reduced to one multipole index $L$, and the $L> 0$ modes are induced only by the RSD or AP effects. Our formalism has two advantages: (1) we can make use of Fast Fourier Transforms (FFTs) to measure the bispectrum; (2) it gives a simple expression to correct for the survey geometry, i.e., the survey window function. As a demonstration, we measure the decomposed bispectrum from the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, and, for the first time, present a $14σ$ detection of the anisotropic bispectrum in the $L=2$ mode.

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arXiv2019

Super-sample tidal modes on the celestial sphere

The super-sample tidal effect carries information on long-wavelength fluctuations that we cannot measure directly. It arises from the mode-coupling between short-wavelength and long-wavelength perturbations beyond a finite region of a galaxy survey and violates statistical isotropy of observed galaxy power spectra. In this paper, we propose the use of bipolar spherical harmonic (BipoSH) decomposition formalism to characterize statistically anisotropic power spectra. Using the BipoSH formalism, we perform a comprehensive study of the effect of the super-sample tides on measurements of other cosmological distortions such as the redshift-space distortion (RSD) and Alcock-Paczyński (AP) effects by means of the Fisher information matrix formalism. We find that the BipoSH formalism can break parameter degeneracies among the super-sample tidal, RSD and AP effects, indicating that the super-sample tides have little impact on the measurements of the RSD and AP effects. We also show that the super-sample tides are detectable with an accuracy better than the $Λ$CDM prediction without impairing the accuracy of measurements of other anisotropies assuming a SPHEREx-like galaxy survey.

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arXiv2018

A direct measure of free electron gas via the Kinematic Sunyaev-Zel'dovich effect in Fourier-space analysis

We present the measurement of the kinematic Sunyaev-Zel'dovich (kSZ) effect in Fourier space, rather than in real space. We measure the density-weighted pairwise kSZ power spectrum, the first use of this promising approach, by cross-correlating a cleaned Cosmic Microwave Background (CMB) temperature map, which jointly uses both Planck Release 2 and Wilkinson Microwave Anisotropy Probe nine-year data, with the two galaxy samples, CMASS and LOWZ, derived fr om the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12. With the current data, we constrain the average optical depth $τ$ multiplied by the ratio of the Hubble parameter at redshift $z$ and the present day, $E=H/H_0$; we find $τE = (3.95\pm1.62)\times10^{-5}$ for LOWZ and $τE = ( 1.25\pm 1.06)\times10^{-5}$ for CMASS, with the optimal angular radius of an aperture photometry filter to estimate the CMB temperature distortion associ ated with each galaxy. By repeating the pairwise kSZ power analysis for various aperture radii, we measure the optical depth as a function of aperture ra dii. While this analysis results in the kSZ signals with only evidence for a detection, ${\rm S/N}=2.54$ for LOWZ and $1.24$ for CMASS, the combination of future CMB and spectroscopic galaxy surveys should enable precision measurements. We estimate that the combination of CMB-S4 and data from DESI shoul d yield detections of the kSZ signal with ${\rm S/N}=70-100$, depending on the resolution of CMB-S4.

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arXiv2017

Limits on statistical anisotropy from BOSS DR12 galaxies using bipolar spherical harmonics

We measure statistically anisotropic signatures imprinted in three-dimensional galaxy clustering using bipolar spherical harmonics (BipoSHs) in both Fourier space and configuration space. We then constrain a well-known quadrupolar anisotropy parameter $g_{2M}$ in the primordial power spectrum, parametrized by $P(\vec{k}) = \bar{P}(k) [ 1 + \sum_{M} g_{2M} Y_{2M}(\hat{k}) ]$, with $M$ determining the direction of the anisotropy. Such an anisotropic signal is easily contaminated by artificial asymmetries due to specific survey geometry. We precisely estimate the contaminated signal and finally subtract it from the data. Using the galaxy samples obtained by the Baryon Oscillation Spectroscopic Survey Data Release 12, we find no evidence for violation of statistical isotropy, $g_{2M}$ for all $M$ to be of zero within the $2σ$ level. The $g_{2M}$-type anisotropy can originate from the primordial curvature power spectrum involving a directional-dependent modulation $g_* (\hat{k} \cdot \hat{p})^2$. The bound on $g_{2M}$ is translated into $g_*$ as $-0.09 < g_* < 0.08$ with a $95\%$ confidence level when $\hat{p}$ is marginalized over.

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arXiv2017

Polypolar spherical harmonic decomposition of galaxy correlators in redshift space: Toward testing cosmic rotational symmetry

We propose an efficient way to test rotational invariance in the cosmological perturbations by use of galaxy correlation functions. In symmetry-breaking cases, the galaxy power spectrum can have extra angular dependence in addition to the usual one due to the redshift-space distortion, $ \hat{k} \cdot \hat{n}$. We confirm that, via the decomposition into not the usual Legendre basis ${\cal L}_\ell(\hat{k} \cdot \hat{n})$ but the bipolar spherical harmonic one $\{Y_{\ell}(\hat{k}) \otimes Y_{\ell'}(\hat{n})\}_{LM}$, the symmetry-breaking signal can be completely distinguished from the usual isotropic one since the former yields nonvanishing $L \geq 1$ modes but the latter is confined to the $L = 0$ one. As a demonstration, we analyze the signatures due to primordial-origin symmetry breakings such as the well-known quadrupolar-type and dipolar-type power asymmetries and find nonzero $L = 2$ and $1$ modes, respectively. Fisher matrix forecasts of their constraints indicate that the $Planck$-level sensitivity could be achieved by the SDSS or BOSS-CMASS data, and an order-of-magnitude improvement is expected in a near future survey as PFS or Euclid by virtue of an increase in accessible Fourier mode. Our methodology is model-independent and hence applicable to the searches for various types of statistically anisotropic fluctuations.

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arXiv2017

Will Kinematic Sunyaev-Zel'dovich Measurements Enhance the Science Return from Galaxy Redshift Surveys?

Yes. Future CMB experiments such as Advanced ACTPol and CMB-S4 should achieve measurements with S/N of $> 0.1$ for the typical galaxies in redshift surveys. These measurements will provide complementary measurements of the growth rate of large scale structure $f$ and the expansion rate of the Universe $H$ to galaxy clustering measurements. This paper emphasizes that there is significant information in the anisotropy of the relative pairwise kSZ measurements. We expand the relative pairwise kSZ power spectrum in Legendre polynomials and consider up to its octopole. Assuming that the noise in the filtered maps is uncorrelated between the positions of galaxies in the survey, we derive a simple analytic form for the power spectrum covariance of the relative pairwise kSZ temperature in redshift space. While many previous studies have assumed optimistically that the optical depth of the galaxies $τ_{\rm T}$ in the survey is known, we marginalize over $τ_{\rm T}$, to compute constraints on the growth rate $f$ and the expansion rate $H$. For realistic sure parameters, we find that combining kSZ and galaxy redshift survey data reduces the marginalized $1$-$σ$ errors on $H$ and $f$ by $\sim50$-$70\%$ compared to the galaxy-only analysis.

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arXiv2016

Understanding redshift space distortions in density-weighted peculiar velocity

Observations of the kinetic Sunyaev-Zel'dovich (kSZ) effect measure the density-weighted velocity field, a potentially powerful cosmological probe. This paper presents an analytical method to predict the power spectrum and two-point correlation function of the density-weighted velocity in redshift space, the direct observables in kSZ surveys. We show a simple relation between the density power spectrum and the density-weighted velocity power spectrum that holds for both dark matter and halos. Using this relation, we can then extend familiar perturbation expansion techniques to the kSZ power spectrum. One of the most important features of density-weighted velocity statistics in redshift space is the change in sign of the cross-correlation between the density and density-weighted velocity at mildly small scales due to nonlinear redshift space distortions. Our model can explain this characteristic feature without any free parameters. As a result, our results can precisely predict the non-linear behavior of the density-weighted velocity field in redshift space up to $\sim30\ h^{-1} {\rm Mpc}$ for dark matter particles at the redshifts of $z=0.0$, $0.5$, and $1.0$.

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arXiv2014

Using Lagrangian perturbation theory for precision cosmology

We explore the Lagrangian perturbation theory (LPT) at 1-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum in LPT. Our approximate solution has good convergence in the series expansion and enables us to compute the power spectrum in LPT accurately and quickly. Non-linear corrections in the Lagrangian perturbation theory naturally satisfy the law of conservation of mass because the relation between matter density and the displacement vector of dark matter corresponds to the conservation of mass. By matching the 1-loop solution in LPT to the 2-loop solution in standard perturbation theory, we present an approximate solution of the power spectrum which has higher order corrections than the 2-loop order in standard perturbation theory with the conservation of mass satisfied. With this approximation, we can use LPT to compute a non-linear power spectrum without any free parameters, and this solution agrees with numerical simulations at $k=0.2$ $h{\rm Mpc}^{-1}$ and $z=0.35$ to better than 2%.

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arXiv2014

How does non-linear dynamics affect the baryon acoustic oscillation?

We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-$k$ solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-$k$ solutions, some of the recently proposed improved perturbation theories do not guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-$k$ regions.We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at $z=0.35$ as $\sim 7.7\ {\rm Mpc}/h$ and describes the small non-linear shift in the peak position due to the galaxy random motions.

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arXiv2013

Relation between standard perturbation theory and regularized multi-point propagator method

We investigate the relation between the regularized multi-propagator method, called "Reg PT", and the standard perturbation theory. Reg PT is one of the most successful models to describe nonlinear evolution of dark matter fluctuations. However, Reg PT is a mathematically unproven interpolation formula between the large-scale solution calculated by the standard perturbation theory and the limiting solution in the small scale calculated by the multi-point propagator method. In this paper, we give an alternative explanation for Reg PT in the context of the standard perturbation theory, showing that Reg PT does not ever have more effective information on nonlinear matter evolution than the standard perturbation theory. In other words, the solutions of the standard perturbation theory reproduce the results of $N$-body simulations better than those of Reg PT, especially at the high-$k$ region. This fact means that the standard perturbation theory at the two-loop level is still one of the best predictions of the nonlinear power spectrum to date. Nevertheless, the standard perturbation theory has not been preferred because of the divergent behavior of the solution at small scales. To solve this problem, we also propose a modified standard perturbation theory which avoids the divergence.

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