  In order to infer the impact of the small-scale physics to the large-scale
properties of the universe, we use a series of cosmological $N$-body
simulations of self-gravitating matter inhomogeneities to measure, for the
first time, the response function of such a system defined as a functional
derivative of the nonlinear power spectrum with respect to its linear
counterpart. Its measured shape and amplitude are found to be in good agreement
with perturbation theory predictions except for the coupling from small to
large-scale perturbations. The latter is found to be significantly damped,
following a Lorentzian form. These results shed light on validity regime of
perturbation theory calculations giving a useful guideline for regularization
of small scale effects in analytical modeling. Most importantly our result
indicates that the statistical properties of the large-scale structure of the
universe are remarkably insensitive to the details of the small-scale physics,
astrophysical or gravitational, paving the way for the derivation of robust
estimates of theoretical uncertainties on the determination of cosmological
parameters from large-scale survey observations.
