In this contribution we present the preliminary results regarding the non-linear BAO signal in higher-order statistics of the cosmic density field. We use ensembles of N-body simulations to show that the non-linear evolution changes the amplitudes of
the BAO signal, but has a negligible effect on the scale of the BAO feature. The latter observation accompanied by the fact that the BAO feature amplitude roughly doubles as one moves to higher orders, suggests that the higher-order correlation amplitudes can be used as probe of the BAO signal.
The amplitude of cosmological density fluctuations, sigma_8, has been studied and estimated by analysing many cosmological observations. The values of the estimates vary considerably between the various probes. However, different estimators probe the
value of sigma_8 in different cosmological scales and do not take into account the nonlinear evolution of the parameter at late times. We show that estimates of the amplitude of cosmological density fluctuations derived from cosmic flows are systematically higher than those inferred at early epochs from the CMB because of nonlinear evolution at later times. We discuss the past and future evolution of linear and nonlinear perturbations, derive corrections to the value of sigma_8 and compare amplitudes after accounting for these differences.
