A closure theory for nonlinear evolution of cosmological power spectra

We apply a nonlinear statistical method in turbulence to the cosmological perturbation theory and derive a closed set of evolution equations for matter power spectra. The resultant closure equations consistently recover the one-loop results of standard perturbation theory, and beyond that, it is still capable of treating the nonlinear evolution of matter power spectra. We find the exact integral expressions for the solutions of closure equations. These analytic expressions coincide with the renormalized one-loop results presented by Crocce and Scoccimarro apart from the vertex renormalization. By constructing the nonlinear propagator, we analytically evaluate the nonlinear matter power spectra based on the first-order Born approximation of the integral expressions and compare it with those of the renormalized perturbation theory.