  Gravitational clustering in our cosmic vicinity is expected to lead to an
enhancement of the local density of relic neutrinos. We derive expressions for
the neutrino density, using a perturbative approach to kinetic field theory and
perturbative solutions of the Vlasov equation up to second order. Our work
reveals that both formalisms give exactly the same results and can thus be
considered equivalent. Numerical evaluation of the local relic neutrino density
at first and second order provides some fundamental insights into the
frequently applied approach of linear response to neutrino clustering (also
known as the Gilbert equation). Against the naive expectation, including the
second-order contribution does not lead to an improvement of the prediction for
the local relic neutrino density but to a dramatic overestimation. This is
because perturbation theory breaks down in a momentum-dependent fashion and in
particular for densities well below unity.
