  Nonlinear effects are crucial in order to compute the cosmological matter
power spectrum to the accuracy required by future generation surveys. Here, a
new approach is presented, in which the power spectrum, the bispectrum and
higher order correlations, are obtained -- at any redshift and for any momentum
scale -- by integrating a system of differential equations. The method is
similar to the familiar BBGKY hierarchy. Truncating at the level of the
trispectrum, the solution of the equations corresponds to the summation of an
infinite class of perturbative corrections. Compared to other resummation
frameworks, the scheme discussed here is particularly suited to cosmologies
other than LambdaCDM, such as those based on modifications of gravity and those
containing massive neutrinos. As a first application, we compute the Baryonic
Acoustic Oscillation feature of the power spectrum, and compare the results
with perturbation theory, the halo model, and N-body simulations. The
density-velocity and velocity-velocity power spectra are also computed, showing
that they are much less contaminated by nonlinearities than the density-density
one. The approach can be seen as a particular formulation of the
renormalization group, in which time is the flow parameter.
