Fast and accurate collapse-time predictions for collisionless matter

Abstract

We consider the gravitational collapse of collisionless matter seeded by three crossed sine waves with various amplitudes, also in the presence of a linear external tidal field. We explore two theoretical methods that are more efficient than standard Lagrangian perturbation theory (LPT) for resolving shell-crossings, the crossing of particle trajectories. One of the methods completes the truncated LPT series for the displacement field far into the UV regime, thereby exponentially accelerating its convergence while at the same time removing pathological behavior of LPT observed in void regions. The other method exploits normal-form techniques known from catastrophe theory, which amounts here to replacing the sine-wave initial data by its second-order Taylor expansion in space at shell-crossing location. This replacement leads to a speed-up in determining the displacement field by several orders of magnitudes, while still achieving permille-level accuracy in the prediction of the shell-crossing time. The two methods can be used independently, but the overall best performance is achieved when combining them. Lastly, we find accurate formulas for the nonlinear density and for the triaxial evolution of the fluid in the fundamental coordinate system, as well as report a newly established correspondence between perfectly symmetric sine-wave collapse and spherical collapse.

31 pages, 24 figures, v3: added clarifications, matches published version at PRD

References in corpus (20)

• Transients from Initial Conditions in Cosmological Simulations
• The Effective Field Theory of Cosmological Large Scale Structures
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• Dark matter clustering: a simple renormalization group approach
• Separate Universe Simulations
• The fine-grained phase-space structure of Cold Dark Matter halos
• Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering
• Baryonic Acoustic Oscillations via the Renormalization Group
• Perturbation theory and excursion set estimates of the probability distribution function of dark matter, and a method for reconstructing the initial distribution function
• How smooth are particle trajectories in a $\Lambda$CDM Universe?
• Vlasov-Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory
• Cosmological Vlasov-Poisson equations for dark matter: Recent developments and connections to selected plasma problems
• Spherical collapse of dark matter haloes in tidal gravitational fields
• Eye of the Tyger: early-time resonances and singularities in the inviscid Burgers equation
• Cold dark matter protohalo structure around collapse: Lagrangian cosmological perturbation theory versus Vlasov simulations
• Analytical growth functions for cosmic structures in a $\Lambda$CDM Universe
• Improving the Lagrangian perturbative solution for cosmic fluid: Applying Shanks transformation
• Semiclassical catastrophe theory of simple bifurcations
• Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon

Cited by in corpus (4)

• BullFrog: Multi-step perturbation theory as a time integrator for cosmological simulations
• Starting Cosmological Simulations from the Big Bang
• Excursion Sets with a "Perfect" Collapse Model
• Post-collapse Lagrangian perturbation theory in three dimensions