Nonlinear Density Fluctuation Field Theory for Large Scale Structure

TL;DR

This paper develops a nonlinear effective field theory for density fluctuations in large scale structure, providing analytic solutions that match multiple survey results and offering a unified theoretical framework.

Contribution

It introduces a nonlinear density fluctuation field theory with analytic solutions that align with observational data, advancing the understanding of large scale structure formation.

Findings

Analytic solutions for the 2-pt correlation function and power spectrum match survey data.

The model incorporates nonlinear effects beyond Gaussian approximation.

The theory offers a unified explanation for features of 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 \xi(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.