Perturbation theory with dispersion and higher cumulants: Nonlinear regime

We present non-linear solutions of Vlasov Perturbation Theory (VPT), describing gravitational clustering collisionless dark matter with dispersion and higher cumulants induced by orbit crossing. show that VPT can be cast into a form is formally analogous to standard perturbation theory (SPT), but including additional variables, interactions, more complex propagation. kernels have crucial decoupling property: for fixed total momentum, the becomes strongly suppressed when any individual momenta cross scale regime. This screening UV modes allows us compute corrections power spectra even cosmologies very blue power-law input spectra, which SPT diverges. compare predictions density velocity divergence as well bispectrum at one-loop order N-body results in scaling universe spectral indices $-1\leq n_s\leq +2$. find good agreement up all cases, reach increases index $n_s$. discuss generation vorticity vector tensor dispersion, showing neglecting would lead violation momentum conservation. verify conservation vorticity, spectrum two-loop order, necessary recover correct large-scale limit slope $n_w=2$. Comparing our measurements confirms cross-over from $k^4$ $k^2$ on large scales. Our provide proof-of-principle perturbative techniques systematically improved based known underlying dynamics.