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We apply a non-linear statistical method in turbulence to the cosmologicalperturbation theory and derive a closed set of evolution equations for matterpower spectra. The resultant closure equations consistently recover theone-loop results of standard perturbation theory and beyond that, it is stillcapable of treating the non-linear evolution of matter power spectra. We findthe exact integral expressions for the solutions of closure equations. Theseanalytic expressions coincide with the renormalized one-loop results presentedby Crocce & Scoccimarro (2006,2007). By constructing the non-linear propagator,we analytically evaluate the non-linear matter power spectra based on thefirst-order Born approximation of the integral expressions and compare it withthose of the renormalized perturbation theory.

A Closure Theory for Non-linear Evolution of Cosmological Power Spectra