All-Sky Analysis of the General Relativistic Galaxy Power Spectrum
arXiv:1301.4501 · doi:10.1103/PhysRevD.88.023502
Abstract
We perform an all-sky analysis of the general relativistic galaxy power spectrum using the well-developed spherical Fourier decomposition. Spherical Fourier analysis expresses the observed galaxy fluctuation in terms of the spherical harmonics and spherical Bessel functions that are angular and radial eigenfunctions of the Helmholtz equation, providing a natural orthogonal basis for all-sky analysis of the large-scale mode measurements. Accounting for all the relativistic effects in galaxy clustering, we compute the spherical power spectrum and its covariance matrix and compare it to the standard three-dimensional power spectrum to establish a connection. The spherical power spectrum recovers the three-dimensional power spectrum at each wavenumber k with its angular dependence mu_k encoded in angular multipole l, and the contributions of the line-of-sight projection to galaxy clustering such as the gravitational lensing effect can be readily accommodated in the spherical Fourier analysis. A complete list of formulas for computing the relativistic spherical galaxy power spectrum is also presented.
19 pages, 5 figures, published in PRD
References in corpus (12)
- Extended Limber Approximation
- Measuring primordial non-gaussianity without cosmic variance
- New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
- Testing General Relativity with 21 cm intensity mapping
- Measuring the matter density using baryon oscillations in the SDSS
- Going beyond the Kaiser redshift-space distortion formula: a full general relativistic account of the effects and their detectability in galaxy clustering
- How to suppress the shot noise in galaxy surveys
- Beyond the plane-parallel and Newtonian approach: Wide-angle redshift distortions and convergence in general relativity
- Relativistic effects in galaxy clustering in a parametrized post-Friedmann universe
- Anisotropic Magnification Distortion of the 3D Galaxy Correlation: II. Fourier and Redshift Space
- Complete Treatment of Galaxy Two-Point Statistics: Gravitational Lensing Effects and Redshift-Space Distortions
- A new method for the Alcock-Paczynski test
Cited by in corpus (53)
- Large-Scale Galaxy Bias
- Ultra large-scale cosmology in next-generation experiments with single tracers
- Beyond the Linear-Order Relativistic Effect in Galaxy Clustering: Second-Order Gauge-Invariant Formalism
- Cosmology on Ultralarge Scales with Intensity Mapping of the Neutral Hydrogen 21 cm Emission: Limits on Primordial Non-Gaussianity
- Effect of nonlinearity between density and curvature perturbations on the primordial black hole formation
- Wide Angle Effects in Future Galaxy Surveys
- Cosmological Measurements with General Relativistic Galaxy Correlations
- Measuring the lensing potential with tomographic galaxy number counts
- The observed galaxy power spectrum in General Relativity
- Relativistic Effect in Galaxy Clustering
- Observed galaxy number counts on the lightcone up to second order: II. Derivation
- Probing the imprint of interacting dark energy on very large scales
- Spherical Harmonic Analyses of Intensity Mapping Power Spectra
- Large-Scale Structure Observables in General Relativity
- Gravity at the horizon: on relativistic effects, CMB-LSS correlations and ultra-large scales in Horndeski's theory
- Exploring galaxies-gravitational waves cross-correlations as an astrophysical probe
- Beware of commonly used approximations I: errors in forecasts
- Relativistic wide-angle galaxy bispectrum on the light-cone
- Simulated multi-tracer analyses with HI intensity mapping
- Impact of Relativistic Effects on the Primordial Non-Gaussianity Signature in the Large-Scale Clustering of Quasars
- The Full-Sky Angular Bispectrum in Redshift Space
- Galaxy Power Spectrum in General Relativity
- Galaxy Two-Point Correlation Function in General Relativity
- 3-dimensional spherical analyses of cosmological spectroscopic surveys
- Clustering of quintessence on horizon scales and its imprint on HI intensity mapping
- SuperFaB: a fabulous code for Spherical Fourier-Bessel decomposition
- 3D galaxy clustering with future wide-field surveys: Advantages of a spherical Fourier-Bessel analysis
- Effects of Linear Redshift Space Distortions and Perturbation Theory on BAOs: A 3D Spherical Analysis
- Wide angle effects for peculiar velocities
- Cross-correlating 2D and 3D galaxy surveys
- Extracting the late-time kinetic Sunyaev-Zel'dovich effect
- Light-Cone Observables and Gauge-Invariance in the Geodesic Light-Cone Formalism
- Generalisation of the Kaiser Rocket effect in general relativity in the wide-angle galaxy 2-point correlation function
- Hybrid-basis inference for large-scale galaxy clustering: combining spherical and Cartesian Fourier analyses
- Cosmological Information Contents on the Light-Cone
- Observing relativistic features in large-scale structure surveys -- II: Doppler magnification in an ensemble of relativistic simulations
- Constraining low redshift [CII] Emission by Cross-Correlating FIRAS and BOSS Data
- Dark energy homogeneity in general relativity: Are we applying it correctly?
- Joint analyses of 2D CMB lensing and 3D galaxy clustering in the spherical Fourier-Bessel basis
- Statistics of a single sky: constrained random fields and the imprint of Bardeen potentials on galaxy clustering
- The full-sky Spherical Fourier-Bessel power spectrum in general relativity
- Large-scale imprint of relativistic effects in the cosmic magnification
- Exact Modeling of Power Spectrum Multipole through Spherical Fourier-Bessel Basis
- Maximum Cosmological Information from Type-Ia Supernova Observations
- Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole
- Reconstructing the Thermal Sunyaev-Zel'dovich Effect in 3D
- Full-Sky Lensing Reconstruction of 21 cm Intensity Maps
- Euclid preparation. The impact of relativistic redshift-space distortions on two-point clustering statistics from the Euclid wide spectroscopic survey
- Understanding the relativistic overdensity of galaxy surveys
- Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum
- Separating Angular and Radial Modes with Spherical-Fourier Bessel Power Spectrum on All Scales and Implications for Systematics Mitigation
- Non-Gaussianity in the Squeezed Three-Point Correlation from the Relativistic Effects
- The Kaiser-Rocket effect: three decades and counting