Modelling non-linear evolution using Lagrangian Perturbation Theory (LPT) re-expansions

Abstract

We present a new method to calculate formation of cosmological structure in the Newtonian limit. The method is based on Lagrangian perturbation theory plus two key theoretical extensions. One advance involves identifying and fixing a previously ignored gauge-like degree of freedom relating quantities calculated in LPT to those measured by a preferred Friedmann-Robertson-Walker (FRW) observer. Handling this connection between calculational and observer frames is physically essential and ensures a momentum conserving description. The second extension is to systematically re-expand the equations of motion to increase LPT's radius of convergence to the maximum future time prior to orbit crossing. The paper implements a complete algorithm and performs extensive "proof of principle" tests of the new method, including direct comparison to known solutions, evaluation of conserved quantities and formal convergence studies. All are satisfactory. We show convergence is exponential in grid size and Lagrangian order and polynomial in step size. There are three {\it powerful advantages} afforded by the new technique: (1) it employs a smooth representation of all fields and the results are not limited by particle induced shot-noise errors, (2) it permits the numerical error to be controlled by changing Lagrangian order and/or number of steps allowing, in principle, arbitrarily small errors to be achieved prior to orbit crossing and (3) it handles generic cold initial data (any periodic density and velocity fields, including those with initial rotational components). Together, these properties make the new technique well-suited to handle quasi-linear scales where analytic methods and/or numerical simulations fail to provide suitably accurate answers.

31 pages, 8 figrues, 2 tables. Accepted in MNRAS

References in corpus (11)

• A test of the nature of cosmic acceleration using galaxy redshift distortions
• Transients from Initial Conditions in Cosmological Simulations
• Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• A critical look at cosmological perturbation theory techniques
• Modelling redshift space distortions in hierarchical cosmologies
• Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering
• The recursion relation in Lagrangian perturbation theory
• Towards quantitative control on discreteness error in the non-linear regime of cosmological N body simulations
• Lagrangian perturbations and the matter bispectrum II: the resummed one-loop correction to the matter bispectrum
• Non-linear density-velocity divergence relation from phase space dynamics

Cited by in corpus (13)

• Lagrangian theory of structure formation in relativistic cosmology III: gravitoelectric perturbation and solution schemes at any order
• Cosmological Vlasov-Poisson equations for dark matter: Recent developments and connections to selected plasma problems
• Frame dragging and Eulerian frames in General Relativity
• Phase Space dynamics of triaxial collapse: Joint density-velocity evolution
• Analytical growth functions for cosmic structures in a $\Lambda$CDM Universe
• Lagrangian theory of structure formation in relativistic cosmology. V. Irrotational fluids
• One-point probability distribution function from spherical collapse: Early Dark Energy (EDE) vs. $\Lambda$CDM
• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
• Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon
• Non-linear density-velocity dynamics in $f(R)$ gravity from spherical collapse
• Fast and accurate collapse-time predictions for collisionless matter
• Approximate methods for the generation of dark matter halo catalogs in the age of precision cosmology
• Stability analysis of fluid flows using Lagrangian Perturbation Theory (LPT): application to the plane Couette flow