Proper-Time Hypersurface of Non-Relativistic Matter Flows: Galaxy Bias in General Relativity

Abstract

We compute the second-order density fluctuation in the proper-time hypersurface of non-relativistic matter flows and relate it to the galaxy number density fluctuation in general relativity. At the linear order, it is equivalent to the density fluctuation in the comoving synchronous gauge, in which two separate gauge conditions coincide. However, at the second order, the density fluctuations in these gauge conditions differ, while both gauge conditions represent the proper-time hypersurface. Compared to the density fluctuation in the temporal comoving and the spatial C-gauge conditions, the density fluctuation in the commonly used gauge condition ($N=1$ and $N^{\alpha }=0$) violates the mass conservation at the second order. We provide their physical interpretations in each gauge condition by solving the geodesic equation and the nonlinear evolution equations of non-relativistic matter. We apply this finding to the second-order galaxy biasing in general relativity, which complements the second-order relativistic description of galaxy clustering in Yoo & Zaldarriaga (2014).

arXiv comment16 pages, no figures, accepted for publication in PRD

References in corpus (42)

• Efficient Computation of CMB anisotropies in closed FRW models
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• A Line of Sight Approach to Cosmic Microwave Background Anisotropies
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
• Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
• Cosmological perturbations
• The linear power spectrum of observed source number counts
• What galaxy surveys really measure
• Biasing and Hierarchical Statistics in Large-scale Structure
• Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Signatures of Supersymmetry from the Early Universe
• Large-scale clustering of galaxies in general relativity
• Evidence for Quadratic Tidal Tensor Bias from the Halo Bispectrum
• General Relativistic Description of the Observed Galaxy Power Spectrum: Do We Understand What We Measure?
• Second-order Perturbations of the Friedmann World Model
• Renormalized Halo Bias
• Clustering of dark matter tracers: renormalizing the bias parameters
• Galaxy Bias and non-Linear Structure Formation in General Relativity
• 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
• Statistical anisotropy of the curvature perturbation from vector field perturbations
• Beyond the Linear-Order Relativistic Effect in Galaxy Clustering: Second-Order Gauge-Invariant Formalism
• Peak-Background Split, Renormalization, and Galaxy Clustering
• Cosmological evolution in vector-tensor theories of gravity
• Consequences of Symmetries and Consistency Relations in the Large-Scale Structure of the Universe for Non-local bias and Modified Gravity
• Relativistic Effect in Galaxy Clustering
• Observed galaxy number counts on the lightcone up to second order: II. Derivation
• Non-Gaussian initial conditions in $\Lambda$CDM: Newtonian, relativistic and primordial contributions
• Complete Treatment of Galaxy Two-Point Statistics: Gravitational Lensing Effects and Redshift-Space Distortions
• Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multi-component, curvature, and rotation
• Third order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects
• Second-order perturbations of a zero-pressure cosmological medium: comoving vs. synchronous gauge
• Second order perturbations of a zero-pressure cosmological medium: Proofs of the relativistic-Newtonian correspondence
• The Sachs-Wolfe Effect: Gauge Independence and a General Expression
• General relativistic effects on non-linear power spectra
• Frame dragging and Eulerian frames in General Relativity
• Second order density perturbations for dust cosmologies
• Non-linear matter bispectrum in general relativity
• Third-order cosmological perturbations of zero-pressure multi-component fluids: Pure general relativistic nonlinear effects

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• Viable Gauge Choices in Cosmologies with Non-Linear Structures
• Relativistic cosmological large scale structures at one-loop
• Gauge-Invariant Formalism of Cosmological Weak Lensing
• Exact non-linear equations for cosmological perturbations
• Cosmological Information Contents on the Light-Cone
• Monopole Fluctuation of the CMB and its Gauge Invariance
• Relativistic effects and primordial non-Gaussianity in the matter density fluctuation
• Exact Analytic Solution for Non-Linear Density Fluctuation in a LCDM Universe
• A Relativistic Interpretation of Bias in Newtonian Simulations
• Relativistic perturbations in $\Lambda$CDM: Eulerian & Lagrangian approaches
• Contributions from primordial non-Gaussianity and General Relativity to the galaxy power spectrum
• From matter to galaxies: General relativistic bias for the one-loop bispectrum
• Long gradient mode and large-scale structure observables
• Non-linear power spectra in the synchronous gauge
• Incompatibility of Standard Galaxy Bias Models in General Relativity
• Dark energy and non-linear power spectrum
• Large scale structures: from inflation to today: a brief report
• Cosmic Dipoles from Large-Scale Structure Surveys
• Non-Gaussianity in the Squeezed Three-Point Correlation from the Relativistic Effects