论文标题
星系的三点相关函数的非线性场方程
The nonlinear field equation of the three-point correlation function of galaxies
论文作者
论文摘要
基于牛顿重力下的密度波动的场理论，我们通过分析获得了3-PT相关函数的非线性方程$ζ$ $ζ$在同质，各向同性，静态宇宙中。密度波动一直保持到二阶。通过煎炸式ANSATZ和Groth-Peebles Ansatz，$ζ$的方程式被关闭，与高斯近似方程式不同。使用从SDSS的数据推断出的边界条件，我们在固定$ u = 2 $处获得解决方案$ζ（r，u，θ）$，该$ u = 2 $，它沿着角度$θ$显示出浅$ u $ $ $ $ - u $ $ shape，尽管如此，沿着径向$ r $ r $单调的降低。我们显示了它与高斯解决方案的差异。作为非高斯性的直接标准，减少的$ q（r，u，θ）$偏离了高斯平面$ q = 1 $，沿$θ$表现出更深的$ u $ $ $ shape，并且沿$ r $差异很弱，同意观察到的数据。
Based on the field theory of density fluctuation under Newtonian gravity, we obtain analytically the nonlinear equation of 3-pt correlation function $ζ$ 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 $ζ$ becomes closed and differs from the Gaussian approximate equation. Using the boundary condition inferred from the data of SDSS, we obtain the solution $ζ(r, u, θ)$ at fixed $u=2$, which exhibits a shallow $U$-shape along the angle $θ$ 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 $Q(r, u, θ)$ deviates from the Gaussianity plane $Q=1$, exhibits a deeper $U$-shape along $θ$ and varies weakly along $r$, agreeing with the observed data.
