The nonlinear field equation of the three-point correlation function of galaxies

Abstract

Based on the field theory of density fluctuation under Newtonian gravity, we obtain analytically the nonlinear equation of 3-pt correlation function $\zeta$ of galaxies in a homogeneous, isotropic, static universe. The density fluctuations have been kept up to second order. By the Fry-Peebles ansatz and the Groth-Peebles ansatz, the equation of $\zeta$ becomes closed and differs from the Gaussian approximate equation. Using the boundary condition inferred from the data of SDSS, we obtain the solution $\zeta (r,u,\theta )$ at fixed $u=2$, which exhibits a shallow $U$-shape along the angle $\theta$ and, nevertheless, decreases monotonously along the radial $r$. We show its difference with the Gaussian solution. As a direct criterion of non-Gaussianity, the reduced $Q(r,u,\theta )$ deviates from the Gaussianity plane $Q=1$, exhibits a deeper $U$-shape along $\theta$ and varies weakly along $r$, agreeing with the observed data.

arXiv comment11 pages, 6 figures

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• Point-splitting regularization of the stress tensor of a coupling scalar field in de Sitter space
• Second-order cosmological perturbations produced by scalar-scalar coupling during inflation stage
• 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