大尺度结构的非线性密度涨落场论
Nonlinear Density Fluctuation Field Theory for Large Scale Structure
摘要：
本文发展了牛顿自引力N体系统准平衡态密度涨落的有效场论，并将其应用于具有小密度涨落的均匀宇宙。在保持密度涨落为二阶的条件下，得到了包含3-pt关联和形式紫外发散的2-pt关联的非线性场方程.通过Groth-Peebles层次分析和质量重整化，方程在高斯近似之外增加了两个新的项，并以它们的系数为参数。利用超几何函数得到了解析解，并进行了数值验证。利用一组固定的两个参数，相关性$ξ(r)$和相应的功率谱P（k）同时匹配来自所有主要勘测（例如APM、SDSS、2dfGRS和REFLEX）的结果。该模型从场论的角度对大尺度结构的几个看似无关的特征给出了统一的理解。这一理论值得推广应用于研究膨胀宇宙中的演化效应。
英文摘要：
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 $ξ(r)$ 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.
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