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

Abstract

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 ${\mathcal{L}}_{\ell }(\hat{k}\cdot \hat{n})$ but the bipolar spherical harmonic one $\{Y_{\ell }(\hat{k})\otimes Y_{{\ell }^{\prime }}(\hat{n}){\}}_{LM}$, the symmetry-breaking signal can be completely distinguished from the usual isotropic one since the former yields nonvanishing $L\ge 1$ 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.

arXiv comment13 pages, 2 figures, 3 tables; version matching publication in PRD

References in corpus (78)

• Planck 2015 results. XIII. Cosmological parameters
• The Seventh Data Release of the Sloan Digital Sky Survey
• SDSS-III: Massive Spectroscopic Surveys of the Distant Universe, the Milky Way Galaxy, and Extra-Solar Planetary Systems
• The Baryon Oscillation Spectroscopic Survey of SDSS-III
• Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)
• Spectral Classification and Redshift Measurement for the SDSS-III Baryon Oscillation Spectroscopic Survey
• Planck 2013 results. XXIII. Isotropy and statistics of the CMB
• Planck 2015 results. XVI. Isotropy and statistics of the CMB
• Gauge Fields and Inflation
• The Clustering of Luminous Red Galaxies in the Sloan Digital Sky Survey Imaging Data
• Imprints of a Primordial Preferred Direction on the Microwave Background
• Linear Redshift Distortions: A Review
• Power Spectrum Super-Sample Covariance
• Estimators for CMB Statistical Anisotropy
• The anisotropic power spectrum and bispectrum in the f(phi) F^2 mechanism
• Ameliorating Systematic Uncertainties in the Angular Clustering of Galaxies: A Study using SDSS-III
• Measuring Statistical isotropy of the CMB anisotropy
• A Hemispherical Power Asymmetry from Inflation
• Cosmic Microwave Background Statistics for a Direction-Dependent Primordial Power Spectrum
• A Spherical Harmonic Analysis of Redshift Space
• Statistical Anisotropy from Anisotropic Inflation
• How isotropic is the Universe?
• Cosmic radio dipole from NVSS and WENSS
• Power asymmetry in WMAP and Planck temperature sky maps as measured by a local variance estimator
• Clustering of Sloan Digital Sky Survey III Photometric Luminous Galaxies: The Measurement, Systematics and Cosmological Implications
• Limits on anisotropic inflation from the Planck data
• Redshift Space Distortions of the Correlation Function in Wide Angle Galaxy Surveys
• Clustering Fossils from the Early Universe
• Signatures of anisotropic sources in the squeezed-limit bispectrum of the cosmic microwave background
• Beyond the plane-parallel and Newtonian approach: Wide-angle redshift distortions and convergence in general relativity
• Asymmetric Beams and CMB Statistical Anisotropy
• Constraints on cosmic hemispherical power anomalies from quasars
• Non-Gaussianity and statistical anisotropy from vector field populated inflationary models
• The Pesky Power Asymmetry
• Dipole anisotropy in sky brightness and source count distribution in radio NVSS data
• Wide Angle Redshift Distortions Revisited
• Non-Perturbative Effects of Geometry in Wide-Angle Redshift Distortions
• A Scale-Dependent Power Asymmetry from Isocurvature Perturbations
• Anisotropy in solid inflation
• Super-Sample Signal
• Homogeneity and isotropy in the 2MASS Photometric Redshift catalogue
• The CMB asymmetry from inflation
• Anisotropic imprint of long-wavelength tensor perturbations on cosmic structure
• CMB Power Asymmetry from Non-Gaussian Modulation
• Parity-violating CMB correlators with non-decaying statistical anisotropy
• Parity-violating and anisotropic correlations in pseudoscalar inflation
• δN Formalism in Anisotropic Inflation and Large Anisotropic Bispectrum and Trispectrum
• Large-scale 3D galaxy correlation function and non-Gaussianity
• Non-detection of a statistically anisotropic power spectrum in large-scale structure
• Anisotropic inflation reexamined: upper bound on broken rotational invariance during inflation
• Asymmetric Sky from the Long Mode Modulations
• Microwave Background Correlations from Dipole Anisotropy Modulation
• Parity violation in the CMB trispectrum from the scalar sector
• Odd-Parity Bipolar Spherical Harmonics
• Anisotropy in the all-sky distribution of galaxy morphological types
• Signatures of anisotropic sources in the trispectrum of the cosmic microwave background
• The expected anisotropy in solid inflation
• Statistical Isotropy of CMB Polarization Maps
• Inflationary power asymmetry from primordial domain walls
• A viable explanation of the CMB dipolar statistical anisotropy
• Probing cosmological isotropy with Planck Sunyaev-Zeldovich galaxy clusters
• Weak-lensing by the large scale structure in a spatially anisotropic universe: theory and predictions
• Is there evidence for anomalous dipole anisotropy in the large-scale structure?
• Linearization of homogeneous, nearly-isotropic cosmological models
• Clustering Fossil from Primordial Gravitational Waves in Anisotropic Inflation
• Large Scale Anisotropic Bias from Primordial non-Gaussianity
• Violation of statistical isotropy and homogeneity in the 21-cm power spectrum
• Hemispherical Anomaly from Asymmetric Initial States
• The Anisotropic Line Correlation Function as a Probe of Anisotropies in Galaxy Surveys
• Angular dependence of primordial trispectra and CMB spectral distortions
• Measuring primordial anisotropic correlators with CMB spectral distortions
• Nonlinear Evolution of Anisotropic Cosmological Power
• Weak-lensing $B$-modes as a probe of the isotropy of the universe
• Lensing as a Probe of Early Universe: from CMB to Galaxies
• Anisotropic non-Gaussianity from Rotational Symmetry Breaking Excited Initial States
• Strongly scale-dependent CMB dipolar asymmetry from super-curvature fluctuations
• Antisymmetric galaxy cross-correlations as a cosmological probe
• Primordial inhomogeneities from massive defects during inflation

Cited by in corpus (27)

• A complete FFT-based decomposition formalism for the redshift-space bispectrum
• Detecting higher spin fields through statistical anisotropy in the CMB and galaxy power spectra
• Improving geometric and dynamical constraints on cosmology with intrinsic alignments of galaxies
• ENCORE: An $\mathcal{O}(N_{\mathrm{g}}^2)$ Estimator for Galaxy $N$-Point Correlation Functions
• Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues
• The impact of large-scale tides on cosmological distortions via redshift-space power spectrum
• Limits on statistical anisotropy from BOSS DR12 galaxies using bipolar spherical harmonics
• Intrinsic galaxy alignment from angular dependent primordial non-Gaussianity
• Modal compression of the redshift-space galaxy bispectrum
• Testing physical models for dipolar asymmetry with CMB polarization
• Effective field theory of statistical anisotropies for primordial bispectrum and gravitational waves
• Redshift-space distortions from vector perturbations
• Statistical anisotropy in galaxy ellipticity correlations
• Wide-angle effects on galaxy ellipticity correlations
• Super-sample tidal modes on the celestial sphere
• Testing the scale-dependent hemispherical asymmetry with the 21-cm power spectrum from the epoch of reionization
• Primordial anisotropies from cosmic strings during inflation
• Power spectrum in the presence of large-scale overdensity and tidal fields: breaking azimuthal symmetry
• Minimum variance estimation of galaxy power spectrum in redshift space
• CMB sky for an off-center observer in a local void I: framework for forecasts
• Minimum variance estimation of statistical anisotropy via galaxy survey
• Statistical anisotropy in CMB spectral distortions
• Redshift-space distortions from vector perturbations II: Anisotropic signal
• Parametrizing modified gravities with vector degrees of freedom: anisotropic growth and lensing
• Closing in on the large-scale CMB power asymmetry
• Testing for gravitational preferred directions with galaxy and lensing surveys
• Probing dipolar power asymmetry with galaxy clustering and intrinsic alignments