http://arxiv.org/abs/1805.08787
Perturbation theory is often used to describe gravitational dynamics of the large scale structure of the Universe in the weakly nonlinear regime and is valid in the single flow regime. However little is known on how the perturbative series expansion performs when the system reaches a significant level of nonlinearity, in particular when approaching shell crossing. To study this issue, we consider the growth of primordial dark matter halos seeded by three crossed initial sine waves of various amplitudes. Using a Lagrangian treatment of cosmological gravitational dynamics, we examine the convergence properties of a high-order perturbative expansion in the vicinity of shell-crossing by comparing the analytical results with state-of-the-art Vlasov-Poisson simulations. In agreement with intuition, we show that convergence of the perturbative series is the best in quasi one-dimensional shell-crossing (one sine-wave dominating) and slows down drastically when approaching triaxial symmetry (three sine-waves with same amplitude). In all cases, however, the perturbative series exhibit a generic behavior as a function of the order of the expansion, which can be fitted with a simple analytic form, allowing us to formally extrapolate the expansion to infinite order. The results of such an extrapolation agree remarkably well with the simulations, even at shell-crossing.
S. Saga, A. Taruya and S. Colombi
Thu, 24 May 18
46/58
Comments: 6 pages, 3 figures
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