  A new computational scheme for the nonlinear cosmological matter power
spectrum (PS) is presented. 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 approximations inherent to this approach as well
as its relations to 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.
