Nonlinear Density Fluctuation Field Theory for Large Scale Structure

Abstract

We develop the effective field theory of density fluctuations for a Newtonian self-gravitating N-body system in quasi-equilibrium, apply it to a homogeneous universe with small density fluctuations. Keeping the density fluctuation up to the second order, we obtain the nonlinear field equation of the 2-pt correlation ξ(r), which contains the 3-pt correlation and formal ultra-violet divergences. By the Groth-Peebles hierarchical ansatz and the mass renormalization, the equation becomes closed with two new terms beyond the Gaussian approximation, and their coefficients are taken as parameters. The analytic solution is obtained in terms of the hypergeometric functions, which is checked numerically. With one single set of fixed two parameters, the correlation $\xi (r)$ and the corresponding power spectrum P(k) match simultaneously the results from all the major surveys, such as APM, SDSS, 2dfGRS, and REFLEX. The model gives a unifying understanding of several seemingly unrelated features of large scale structure from a field-theoretical perspective. The theory is worthy to be extended to study the evolution effects in an expanding universe.

16 pages, 7 figures. to appear in Chin. J. Astron. Astrophys

References in corpus (30)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Simulating the joint evolution of quasars, galaxies and their large-scale distribution
• The 2dF Galaxy Redshift Survey: Spectra and redshifts
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• The 3D power spectrum of galaxies from the SDSS
• The Luminosity and Color Dependence of the Galaxy Correlation Function
• The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe
• Galaxy Clustering in Early SDSS Redshift Data
• The 2dF Galaxy Redshift Survey: galaxy clustering per spectral type
• A 120-Mpc Periodicity in the Three-Dimensional Distribution of Galaxy Superclusters
• The APM Galaxy Survey III: An Analysis of Systematic Errors in the Angular Correlation Function and Cosmological Implications
• The ROSAT-ESO Flux Limited X-ray (REFLEX) Galaxy Cluster Survey II: The Spatial Correlation Function
• The richness dependence of galaxy cluster correlations: Results from a redshift survey of rich APM clusters
• The Richness-Dependent Cluster Correlation Function: Early SDSS Data
• The Las Campanas Redshift Survey Galaxy-Galaxy Autocorrelation Function
• The Three-point Correlation Function of Galaxies Determined from the Las Campanas Redshift Survey
• Analytic approach to the CMB polarizations generated by relic gravitational waves
• The ROSAT-ESO Flux-Limited X-Ray (REFLEX) Galaxy Cluster Survey III: The Power Spectrum
• The Three-point Correlation Function of Galaxies Determined from the 2dF Galaxy Redshift Survey
• A new approach to gravitational clustering: a path-integral formalism and large-N expansions
• The supercluster--void network II. An oscillating cluster correlation function
• Analytic Spectra of CMB Anisotropies and Polarization Generated by Relic Gravitational Waves with Modification due to Neutrino Free-Streaming
• The Las Campanas Distant Cluster Survey -- The Correlation Function
• Galaxy groups in the 2dF galaxy redshift survey: Large Scale Structure with Groups
• Optical and X-ray clusters as tracers of the supercluster-void network. III Distribution of Abell and APM clusters
• Optical and X-ray clusters as tracers of the supercluster-void network. II The spatial correlation function
• The power spectrum of galaxy clustering in the APM survey
• Markov-chain reconstruction of the 2dF Galaxy Redshift Survey real-space power spectrum
• A Coarse-Grained Field Theory for Density Fluctuations and Correlation Functions of Galactic Objects

Cited by in corpus (9)

• Second-order cosmological perturbations. IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stage
• Field Theory of the Correlation Function of Mass Density Fluctuations for Self-Gravitating Systems
• Point-splitting regularization of the stress tensor of a coupling scalar field in de Sitter space
• Second-order cosmological perturbations. III. Produced by scalar-scalar coupling during radiation-dominated stage
• Second-order cosmological perturbations produced by scalar-scalar coupling during inflation stage
• The nonlinear field equation of the three-point correlation function of galaxies
• Analytical Equation of Three-point Correlation Function of Galaxies: to Third Order of Density Perturbation
• The equation and solution of 4-point correlation function of galaxies in Gaussian approximation and its parity-odd part
• The nonlinear equation of correlation function of galaxies in the expanding universe and the solution in linear approximation