Galaxy Power Spectrum in General Relativity

Abstract

We present the galaxy power spectrum in general relativity. Using a novel approach, we derive the galaxy power spectrum taking into account all the relativistic effects in observations. In particular, we show independently of survey geometry that relativistic effects yield no divergent terms (proportional to $k^{-4}{P}_m(k)$ or $k^{-2}{P}_m(k)$ on all scales) that would mimic the signal of primordial non-Gaussianity. This cancellation of such divergent terms is indeed expected from the equivalence principle, meaning that any perturbation acting as a uniform gravity on the scale of the experiment cannot be measured. We find that the unphysical infrared divergence obtained in previous calculations occurred only due to not considering all general relativistic contributions consistently. Despite the absence of divergent terms, general relativistic effects represented by non-divergent terms alter the galaxy power spectrum at large scales (smaller than the horizon scale). In our numerical computation of the full galaxy power spectrum, we show the deviations from the standard redshift-space power spectrum due to these non-divergent corrections. We conclude that, as relativistic effects significantly alter the galaxy power spectrum at $k\lesssim k_{eq}$, they need to be taken into account in the analysis of large-scale data.

arXiv comment29 pages, 10 figures, accepted for publication in JCAP

References in corpus (38)

• The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
• Observational Probes of Cosmic Acceleration
• Cosmology and Fundamental Physics with the Euclid Satellite
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Redshift-Space Distortions, Pairwise Velocities and Nonlinearities
• The linear power spectrum of observed source number counts
• What galaxy surveys really measure
• Reconstructing the history of structure formation using redshift distortions
• Science with the Square Kilometer Array: Motivation, Key Science Projects, Standards and Assumptions
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Testing cosmological structure formation using redshift-space distortions
• Large-scale clustering of galaxies in general relativity
• General Relativistic Description of the Observed Galaxy Power Spectrum: Do We Understand What We Measure?
• Constraining primordial non-Gaussianity with future galaxy surveys
• Fourier Analysis of Redshift Space Distortions and the Determination of Omega
• Testing General Relativity on Horizon Scales and the Primordial non-Gaussianity
• Going beyond the Kaiser redshift-space distortion formula: a full general relativistic account of the effects and their detectability in galaxy clustering
• Disentangling non-Gaussianity, bias and GR effects in the galaxy distribution
• Primordial non-Gaussianity in the Bispectrum of the Halo Density Field
• Cosmic Rulers
• Optimal Constraints on Local Primordial Non-Gaussianity from the Two-Point Statistics of Large-Scale Structure
• Wide Angle Effects in Future Galaxy Surveys
• The full-sky relativistic correlation function and power spectrum of galaxy number counts: I. Theoretical aspects
• Constraints on Primordial Non-Gaussianity from Large Scale Structure Probes
• All-Sky Analysis of the General Relativistic Galaxy Power Spectrum
• Relativistic Effect in Galaxy Clustering
• Anisotropic Magnification Distortion of the 3D Galaxy Correlation: II. Fourier and Redshift Space
• Gauge-Invariance and Infrared Divergences in the Luminosity Distance
• COFFE: a code for the full-sky relativistic galaxy correlation function
• Galaxy Two-Point Correlation Function in General Relativity
• Relativistic corrections and non-Gaussianity in radio continuum surveys
• Relativistic effects and primordial non-Gaussianity in the galaxy bias
• A relativistic signature in large-scale structure
• General and consistent statistics for cosmological observations
• General relativistic corrections and non-Gaussianity in large scale structure
• Measuring BAO and non-Gaussianity via QSO clustering
• Exact Analytic Solution for Non-Linear Density Fluctuation in a LCDM Universe
• Relativistic effects and primordial non-Gaussianity in the matter density fluctuation

Cited by in corpus (30)

• The observed galaxy power spectrum in General Relativity
• Baryon Acoustic Oscillation Theory and Modelling Systematics for the DESI 2024 results
• Growth of Cosmic Structure
• Wide-angle and relativistic effects in Fourier-space clustering statistics
• Local primordial non-Gaussianity in the relativistic galaxy bispectrum
• Large Scale Limit of the Observed Galaxy Power Spectrum
• Monopole Fluctuation of the CMB and its Gauge Invariance
• Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole
• Decoupling Local Primordial non-Gaussianity from Relativistic Effects in the Galaxy Bispectrum
• Infrared (in)sensitivity of relativistic effects in cosmological observable statistics
• Primordial non-Gaussianity -- the effects of relativistic and wide-angle corrections to the power spectrum
• Relativistic and wide-angle corrections to galaxy power spectra
• Conditions for the Absence of Infrared Sensitivity in Cosmological Probes in Any Gravity Theories
• Contributions from primordial non-Gaussianity and General Relativity to the galaxy power spectrum
• Large gauge transformations, local coordinates and cosmological observables
• Relativistic matter bispectrum of cosmic structures on the light cone
• Incompatibility of Standard Galaxy Bias Models in General Relativity
• Lensing convergence and anisotropic dark energy in galaxy redshift surveys
• Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum
• Gravitational Redshift from Galaxy Clusters -- a Relativistic Approach
• Monopole Fluctuations in Galaxy Surveys
• A Light-Cone Approach to Higher-Order Cosmological Observables
• Infrared Sensitivity of Cosmological Probes in Horndeski Theory
• A Simple, Exact Formulation of Number Counts in the Geodesic-Light-Cone Gauge
• Detecting Local and Integrated Relativistic Effects by Multi-Tracing a Single Galaxy Population in Harmonic Space
• Large-scale Modeling of the Observed Power Spectrum Multipoles
• Gravitational redshift from large-scale structure: nonlinearities, antisymmetries, and the dipole
• Living in a Non-Flat Universe: Theoretical Formalism
• Non-Gaussianity in the Squeezed Three-Point Correlation from the Relativistic Effects
• Cosmic Dipoles from Large-Scale Structure Surveys