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We present a coarse-grained field theory of density fluctuations for aNewtonian self-gravitating many-body system and apply it to a homogeneousUniverse with small density fluctuations. The theory treats the clustering ofgalaxies and clusters in terms of the field of density fluctuations. The Jeanslength $\lambda_0$, a unique physical scale for a gravitating system, appearsnaturally as the characteristic scale underlying the large scale structure.Under Gaussian approximation the analytic expressions of $\xi(r)$ and $P(k)$are obtained. The correlation amplitude is proportional to the galactic mass,and is oscillating over large scales $\sim 100$ $h^{-1}$ Mpc and damped tozero. The spectrum amplitude is inversely proportional to the galactic numberdensity.The preliminary results qualitatively explain some pronounced featuresof large scale structures.Comment: 7 pages, 4 figures. to appear in A&

A coarse-grained field theory for density fluctuations and correlation functions of galaxies and clusters