Flowing with time: a new approach to non-linear cosmological perturbations

Abstract

Non-linear effects are crucial for computing 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 that of the familiar BBGKY (Bogoliubov–Born–Green–Kirkwood–Yvon) 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 ΛCDM (CDM: cold dark matter), 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, revealing that they are much less contaminated by non-linearities 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.