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.

11 pages, 6 figures

References in corpus (7)

• The Effect of Large-Scale Structure on the SDSS Galaxy Three-Point Correlation Function
• Three-Point Correlation Functions of SDSS Galaxies: Luminosity and Color Dependence in Redshift and Projected Space
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• The equation and solution of 4-point correlation function of galaxies in Gaussian approximation and its parity-odd part