Nonlinear density fluctuation field theory for large scale structure

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.

Fractal dimension and thermodynamic fluctuation properties of IDV light curves

Fractals are a basic tool for phenomenologicalty describing natural ob- jects having a high degree of temporal or spatial variability. From a physical point of view the fractal properties of natural systems can also be interpreted by using the standard formalism of thermodynamical fluctuations. We introduce and analyze the fractal dimension of the Intra-Day-Variability （IDV） light-curves of BL Lac objects, in the optical, radio and X-ray bands. A general description of the fluctuation spec- trum of these systems based on general thermodynamical principles is also proposed. Based on the general fractal properties of a given physical system, we also introduce the predictability index for the IDV light curves. We have explicitly determined the fractal dimension for the R-band observations of five blazars, as well as for the ra- dio band observations of the compact extragalactic radio source J 1128＋5925 and of several X-ray sources. Our results show that the fractal dimension of the optical and X-ray observations indicates an almost pure ＂Brownian noise＂ （random walk） spectrum, with a very low predictability index, while in the radio band the predictability index is much higher. We have also studied the spectral properties of the IDV light curves and we have shown that their spectral index is very closely correlated with the corresponding fractal dimension.