Second-order gauge-invariant formalism for the cosmological observables: Complete verification of their gauge-invariance

Abstract

Accounting for all the relativistic effects, we have developed the fully nonlinear gauge-invariant formalism for describing the cosmological observables and presented the second-order perturbative expressions associated with light propagation and observations without choosing a gauge condition. For the first time, we have performed a complete verification of the validity of our second-order expressions by comparing their gauge-transformation properties from two independent methods: one directly obtained from their expressions in terms of metric perturbations and the other expected from their nonlinear relations. The expressions for the cosmological observables such as galaxy clustering and the luminosity distance are invariant under diffeomorphism and gauge-invariant at the observed position. We compare our results to the previous work and discuss the differences in the perturbative expressions. Our second-order gauge-invariant formalism constitutes a major step forward in the era of precision cosmology and its applications in the future will play a crucial role for going beyond the power spectrum and probing the early universe.

arXiv comment64 pages, 1 figure, accepted for publication in JCAP

References in corpus (87)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• The DESI Experiment Part I: Science,Targeting, and Survey Design
• Non-Gaussianity from Inflation: Theory and Observations
• Weak Gravitational Lensing of the CMB
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Cosmic Microwave Background Anisotropies
• Planck 2018 results. VIII. Gravitational lensing
• Single field consistency relation for the 3-point function
• The linear power spectrum of observed source number counts
• What galaxy surveys really measure
• Relativistic second-order perturbations of the Einstein-de Sitter Universe
• The effect of primordial non-Gaussianity on halo bias
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Large-scale clustering of galaxies in general relativity
• General Relativistic Description of the Observed Galaxy Power Spectrum: Do We Understand What We Measure?
• Correlated Fluctuations in Luminosity Distance and the (Surprising) Importance of Peculiar Motion in Supernova Surveys
• Second-order Perturbations of the Friedmann World Model
• On the consistency relation of the 3-point function in single field inflation
• A Complete Treatment of CMB Anisotropies in a FRW Universe
• Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --
• Light-cone averaging in cosmology: formalism and applications
• Wide-Field InfraRed Survey Telescope (WFIRST) Final Report
• Second Order Corrections to Weak Lensing by Large-Scale Structure
• (Mis-)Interpreting supernovae observations in a lumpy universe
• Beyond the Linear-Order Relativistic Effect in Galaxy Clustering: Second-Order Gauge-Invariant Formalism
• Cosmic Rulers
• Weak lensing power spectra for precision cosmology: Multiple-deflection, reduced shear and lensing bias corrections
• The Effect of Inhomogeneities on the Luminosity Distance-Redshift Relation: is Dark Energy Necessary in a Perturbed Universe?
• Non-Gaussianity beyond slow roll in multi-field inflation
• Galaxy number counts to second order and their bispectrum
• The value of H_0 in the inhomogeneous Universe
• Large-Scale Structure with Gravitational Waves II: Shear
• Do stochastic inhomogeneities affect dark-energy precision measurements?
• Full-sky lensing shear at second order
• Primordial Gravity Waves and Weak Lensing
• Observed galaxy number counts on the lightcone up to second order: I. Main result
• An exact Jacobi map in the geodesic light-cone gauge
• The second-order luminosity-redshift relation in a generic inhomogeneous cosmology
• Theory and Statistics of Weak Lensing from Large-Scale Mass Inhomogeneities
• Effect of Peculiar Motion in Weak Lensing
• The bispectrum of relativistic galaxy number counts
• The Luminosity Distance in Perturbed FLRW Spacetimes
• Relativistic Effect in Galaxy Clustering
• Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification. I - Key results
• Observed galaxy number counts on the lightcone up to second order: II. Derivation
• Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification. II - Derivation
• Average magnification effect of clumping of matter
• The luminosity distance-redshift relation up to second order in the Poisson gauge with anisotropic stress
• Complete Treatment of Galaxy Two-Point Statistics: Gravitational Lensing Effects and Redshift-Space Distortions
• Gauging the cosmic microwave background
• Do we care about the distance to the CMB? Clarifying the impact of second-order lensing
• Non-Gaussianities due to Relativistic Corrections to the Observed Galaxy Bispectrum
• Cosmic shear bispectrum from second-order perturbations in General Relativity
• Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multi-component, curvature, and rotation
• Gauge-Invariance and Infrared Divergences in the Luminosity Distance
• A general relativistic signature in the galaxy bispectrum: the local effects of observing on the lightcone
• CMB-lensing beyond the leading order: temperature and polarization anisotropies
• Observed galaxy number counts on the lightcone up to second order: III. Magnification Bias
• Effect of lensing non-Gaussianity on the CMB power spectra
• Impact of next-to-leading order contributions to CMB lensing
• The observed galaxy bispectrum from single-field inflation in the squeezed limit
• Impact of polarisation on the intrinsic CMB bispectrum
• Second Order Geodesic Corrections to Cosmic Shear
• Vector and Tensor Contributions to the Luminosity Distance
• Full-sky formulae for weak lensing power spectra from total angular momentum method
• On the perturbation of the luminosity distance by peculiar motions
• Non-Gaussianity of Large-Scale Cosmic Microwave Background Anisotropies beyond Perturbation Theory
• Imprints of local lightcone projection effects on the galaxy bispectrum. II
• Non-linear general relativistic effects in the observed redshift
• Gauge-Transformation Properties of Cosmological Observables and its Application to the Light-Cone Average
• $\bar{T}$: A New Cosmological Parameter?
• General and consistent statistics for cosmological observations
• Correlation function of the luminosity distances
• Gauge-Invariant Formalism of Cosmological Weak Lensing
• Lensing signals from Spin-2 perturbations
• Light-Cone Observables and Gauge-Invariance in the Geodesic Light-Cone Formalism
• Geodesic "curve"-of-sight formulae for the cosmic microwave background: a unified treatment of redshift, time delay, and lensing
• Formulating Weak Lensing from the Boltzmann Equation and Application to Lens-lens Couplings
• Jacobi Mapping Approach for a Precise Cosmological Weak Lensing Formalism
• Cutting out the cosmological middle man: General Relativity in the light-cone coordinates
• Exact non-linear equations for cosmological perturbations
• Cosmological Information Contents on the Light-Cone
• Monopole Fluctuation of the CMB and its Gauge Invariance
• Testing inflationary consistency relations by the potential CMB observations
• Full-sky weak lensing: a nonlinear post-Friedmann treatment
• Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole
• General Relativistic Effects in Weak Lensing Angular Power Spectra

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• Decoupling Local Primordial non-Gaussianity from Relativistic Effects in the Galaxy Bispectrum
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• 3+1 formalism of the minimally extended varying speed of light model
• A Light-Cone Approach to Higher-Order Cosmological Observables
• Infrared Sensitivity of Cosmological Probes in Horndeski Theory
• Observable Gravitational Wave Strain at Second Order
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