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.

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

References in corpus (17)

• A Hemispherical Power Asymmetry from Inflation
• Cosmic Microwave Background Statistics for a Direction-Dependent Primordial Power Spectrum
• Power asymmetry in WMAP and Planck temperature sky maps as measured by a local variance estimator
• Asymmetric Beams and CMB Statistical Anisotropy
• Constraints on cosmic hemispherical power anomalies from quasars
• A Scale-Dependent Power Asymmetry from Isocurvature Perturbations
• Super-Sample Signal
• Homogeneity and isotropy in the 2MASS Photometric Redshift catalogue
• Parity-violating and anisotropic correlations in pseudoscalar inflation
• Non-detection of a statistically anisotropic power spectrum in large-scale structure
• Parity violation in the CMB trispectrum from the scalar sector
• Anisotropy in the all-sky distribution of galaxy morphological types
• Statistical Isotropy of CMB Polarization Maps
• Inflationary power asymmetry from primordial domain walls
• Angular dependence of primordial trispectra and CMB spectral distortions
• Nonlinear Evolution of Anisotropic Cosmological Power
• Strongly scale-dependent CMB dipolar asymmetry from super-curvature fluctuations

Cited by in corpus (3)

• Detecting higher spin fields through statistical anisotropy in the CMB and galaxy power spectra
• Wide-angle effects on galaxy ellipticity correlations
• Minimum variance estimation of galaxy power spectrum in redshift space