Stefano Anselmi, Massimo Pietroni
A new computational scheme for the nonlinear cosmological matter power spectrum (PS) is presented. It allows an analytic summation, at all orders in perturbation theory, of the leading contributions at small scales, thus extending to the PS the program initiated by Crocce and Scoccimarro for the nonlinear propagator. Our method is based on evolution equations in time, which can be cast in a form extremely convenient for fast numerical evaluations. A nonlinear PS is obtained in a time comparable to that needed for a simple 1-loop computation, and the numerical implementation is very simple. Our results agree with N-body simulations at the percent level in the BAO range of scales, and at the few-percent level up to $k ~ 1$ h/Mpc at $z >= 0.5$, thereby opening the possibility of applying this tool to scales interesting for weak lensing. We clarify the relation between our approach and previous ones, such as the Time Renormalization Group, and the multi-point propagator expansion. We discuss possible lines of improvements of the method and its intrinsic limitations by multi streaming at small scales and low redshifts.
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http://arxiv.org/abs/1205.2235
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