Exact Analytic Solution for Non-Linear Density Fluctuation in a LCDM Universe

Abstract

We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a $\Lambda$CDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

20 pages, no figures, published in JCAP

References in corpus (14)

• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Beyond the Linear-Order Relativistic Effect in Galaxy Clustering: Second-Order Gauge-Invariant Formalism
• Galaxy number counts to second order and their bispectrum
• Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe
• Relativistic Effect in Galaxy Clustering
• Observed galaxy number counts on the lightcone up to second order: II. Derivation
• 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
• Proper-Time Hypersurface of Non-Relativistic Matter Flows: Galaxy Bias in General Relativity
• Relativistic effects and primordial non-Gaussianity in the matter density fluctuation
• Non-linear matter bispectrum in general relativity
• Nonlinear cosmological power spectra in Einstein's gravity
• Non-linear power spectra in the synchronous gauge

Cited by in corpus (10)

• Galaxy Power Spectrum in General Relativity
• Galaxy Two-Point Correlation Function in General Relativity
• Wide-angle and relativistic effects in Fourier-space clustering statistics
• Correlation function of the luminosity distances
• fNL - gNL mixing in the matter density field at higher orders
• Multi-Scale Perturbation Theory I: Methodology and Leading-Order Bispectrum Corrections in the Matter-Dominated Era
• General Relativistic Effects in Weak Lensing Angular Power Spectra
• Incompatibility of Standard Galaxy Bias Models in General Relativity
• Non-Gaussianity in the Squeezed Three-Point Correlation from the Relativistic Effects
• Cosmic Dipoles from Large-Scale Structure Surveys