Nonlinear wavenumber ($k_{\mathrm{NL}}$)

The nonlinear wavenumber is the inverse scale at which linear density contrast fluctuations become of order unity. For the one-dimensional convention $⟨\delta (k)\delta (k^{\prime })⟩=2\pi {\delta }^{(D)}(k+k^{\prime })P_L(k)$, a usual estimate is $k_{\mathrm{NL}}{P}_L(k_{\mathrm{NL}})/\pi \sim 1$. Loop momenta above this scale require the effective field theory of large-scale structure even when external modes are perturbative.