We develop an effective field theory of density fluctuations for a Newtonian self-gravitating N-body system in quasi-equilibrium and apply it to a homogeneous universe with small density fluctuations. Keeping the dens...We develop an effective field theory of density fluctuations for a Newtonian self-gravitating N-body system in quasi-equilibrium and apply it to a homogeneous universe with small density fluctuations. Keeping the density fluctuations up to second or- der, we obtain the nonlinear field equation of 2-pt correlation ξ（r）, which contains 3-pt correlation and formal ultra-violet divergences. By the Groth-Peebles hierarchical ansatz and 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 two fixed parameters, the correlation ξ（r） and the corresponding power spectrum P（k） simultaneously match 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 worth extending to study the evolution effects in an expanding universe.展开更多
基金supported by the National Natural Science Foundation of China (No.10773009)SRFDP and CAS.
文摘We develop an effective field theory of density fluctuations for a Newtonian self-gravitating N-body system in quasi-equilibrium and apply it to a homogeneous universe with small density fluctuations. Keeping the density fluctuations up to second or- der, we obtain the nonlinear field equation of 2-pt correlation ξ（r）, which contains 3-pt correlation and formal ultra-violet divergences. By the Groth-Peebles hierarchical ansatz and 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 two fixed parameters, the correlation ξ（r） and the corresponding power spectrum P（k） simultaneously match 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 worth extending to study the evolution effects in an expanding universe.
