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, k ·n. We confirm that, via the decomposition into not the usual Legendre basis L (k ·n) but the bipolar spherical harmonic one {Y (k)⊗Y (n)}LM , the symmetry-breaking signal can be completely distinguished from the usual isotropic one since the former yields nonvanishing L ≥ 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.

Super-sample tidal modes on the celestial sphere

“…The final one is related to constraining anisotropic inflation models. Signals due to such models are also present in the L = 2 mode [30][31][32] and hence may be biased by the supersample tides. As has been done in this paper, the distinguishability should be examined for interpreting observational constraints precisely.…”

“…To relate the coefficients of the bipolar spherical harmonic expansion with those of usual Legendre expansion, let us introduce the reduced coefficients defined in Refs. [30,31]…”

“…The Legendre coefficients with subscript (O) denote P (O) 0 (k) = P 0 (k) + 1/n g , P J≥5 (k) = 0 withn g being the local number density of galaxies. By making use of the formulas in Appendix C, the covariance above leads to the following expression of the covariance for the reduced BipoSH coefficients [30],…”

Testing for gravitational preferred directions with galaxy and lensing surveys

“…Preferred directions effects have been explored in the framework of the anisotropic PPN formalism [24] and bounds from laboratory experiments have been obtained in [25]. The possible cosmological implications have been studied both on the CMB temperature power spectrum [4,6] and in the matter distribution in [26][27][28][29]. In those works, the evolution both of the background and perturbations is assumed to be the standard in ΛCDM and the anisotropy is assumed to be present only in the primordial power spectra.…”

Statistical anisotropy in CMB spectral distortions

“…More generally, spinning particles imprint the multipole asymmetry of the primordial correlators [11][12][13], and hence the statistical asymmetries are sensitive to the matter contents during inflation. Thus, the statistical isotropy is an assumption to be tested through observations, and its probes have been discussed with the powerspectra of the CMB anisotropies, the 21cm lines and galaxies [14][15][16][17][18][19][20][21][22][23][24].In this Letter, we point out another way to link the primordial statistical anisotropy with a cosmological observable, i.e., a deviation of the CMB energy spectrum from the blackbody one. In particular, we discuss the sensitivity for the short wavelength (O(0.01) < kMpc < O(1.))…”