Large-Scale Structure Observables in General Relativity

Abstract

We review recent studies that rigorously define several key observables of the large-scale structure of the Universe in a general relativistic context. Specifically, we consider i) redshift perturbation of cosmic clock events; ii) distortion of cosmic rulers, including weak lensing shear and magnification; iii) observed number density of tracers of the large-scale structure. We provide covariant and gauge-invariant expressions of these observables. Our expressions are given for a linearly perturbed flat Friedmann-Robertson-Walker metric including scalar, vector, and tensor metric perturbations. While we restrict ourselves to linear order in perturbation theory, the approach can be straightforwardly generalized to higher order.

24 pages, 3 figures. A review article submitted to CQG focus issue "Relativistic Effects in Cosmology". arXiv admin note: substantial text overlap with arXiv:1204.3625, v2: correct one missing reference

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Cited by in corpus (34)

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• Gauge dependence of gravitational waves generated from scalar perturbations
• General relativistic corrections to $N$-body simulations and the Zel'dovich approximation
• On the impact of galaxy bias uncertainties on primordial non-Gaussianity constraints
• How Gaussian can our Universe be?
• An $n$-th order Lagrangian Forward Model for Large-Scale Structure
• Conformal Fermi Coordinates
• Bayesian field-level inference of primordial non-Gaussianity using next-generation galaxy surveys
• Imprints of Oscillatory Bispectra on Galaxy Clustering
• 2-FAST: Fast and accurate computation of projected two-point functions
• The Impact of Line Misidentification on Cosmological Constraints from Euclid and other Spectroscopic Galaxy Surveys
• Unbiased Cosmological Parameter Estimation from Emission Line Surveys with Interlopers
• Caustics of $1/r^n$ binary gravitational lenses: from galactic haloes to exotic matter
• The Cosmological Perturbation Theory on the Geodesic Light-Cone background
• Vector perturbations of galaxy number counts
• Large-Scale Tides in General Relativity
• The Odd-Parity Galaxy Bispectrum
• Compensated Isocurvature Perturbations in the Galaxy Power Spectrum
• Redshift-space distortions from vector perturbations
• Cosmological nonlinear density and velocity power spectra including nonlinear vector and tensor modes
• Large-scale imprint of relativistic effects in the cosmic magnification
• Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole
• Redshift-space distortions from vector perturbations II: Anisotropic signal
• Relativistic virial relation for cosmological structures
• Long gradient mode and large-scale structure observables
• Reconstructing the Long-wavelength Matter Density Fluctuation Modes from the Scalar-Type Clustering Fossils
• Understanding the relativistic overdensity of galaxy surveys
• Straightening the Ruler: Field-Level Inference of the BAO Scale with LEFTfield
• Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum
• Detecting Relativistic Doppler by Multi-Tracing a Single Galaxy Population
• A Light-Cone Approach to Higher-Order Cosmological Observables
• Observable Gravitational Wave Strain at Second Order
• The Mattig Expression for a d-dimensional Gauss Bonnet FRWL Cosmology
• Detecting Local and Integrated Relativistic Effects by Multi-Tracing a Single Galaxy Population in Harmonic Space