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The power spectrum response function of the large-scale structure of theUniverse describes how the evolved power spectrum is modified by a small changein initial power through non-linear mode coupling of gravitational evolution.It was previously found that the response function for the coupling from smallto large scales is strongly suppressed in amplitude, especially at late times,compared to predictions from perturbation theory (PT) based on thesingle-stream approximation. One obvious explanation for this is that PT failsto describe the dynamics beyond shell-crossing. We test this idea by comparingmeasurements in $N$-body simulations to prescriptions based on PT but augmentedwith adaptive smoothing to account for the formation of non-linear structuresof various sizes in the multi-stream regime. We first start withone-dimensional (1D) cosmology, where the Zel'dovich approximation provides theexact solution in the single stream regime. Similarly to the 3D case, theresponse function of the large-scale modes exhibits a strong suppression inamplitude at small scales which cannot be explained by the Zel'dovich solutionalone. However, by performing adaptive smoothing of initial conditions toidentify haloes of different sizes and solving approximately post-collapsedynamics in the 3-streams regime, agreement between theory and simulationsdrastically improves. We extend our analyses to the 3D case using PINOCCHIOalgorithm, in which similar adaptive smoothing is implemented on the LagrangianPT fields to identify haloes and is combined with a spherical halo prescriptionto account for post-collapse dynamics. Again, a suppression is found in thecoupling between small- and large-scale modes and the agreement withsimulations is improved.

Power spectrum response of large-scale structure in 1D and in 3D: tests of prescriptions for post-collapse dynamics