A fast semi-discrete optimal transport algorithm for a unique reconstruction of the early Universe

Abstract

We leverage powerful mathematical tools stemming from optimal transport theory and transform them into an efficient algorithm to reconstruct the fluctuations of the primordial density field, built on solving the Monge-Ampère-Kantorovich equation. Our algorithm computes the optimal transport between an initial uniform continuous density field, partitioned into Laguerre cells, and a final input set of discrete point masses, linking the early to the late Universe. While existing early universe reconstruction algorithms based on fully discrete combinatorial methods are limited to a few hundred thousand points, our algorithm scales up well beyond this limit, since it takes the form of a well-posed smooth convex optimization problem, solved using a Newton method. We run our algorithm on cosmological $N$-body simulations, from the AbacusCosmos suite, and reconstruct the initial positions of $\mathcal{O}(10^7)$ particles within a few hours with an off-the-shelf personal computer. We show that our method allows a unique, fast and precise recovery of subtle features of the initial power spectrum, such as the baryonic acoustic oscillations.

arXiv comment22 pages

References in corpus (44)

• Planck 2015 results. XIII. Cosmological parameters
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• A 2% Distance to z=0.35 by Reconstructing Baryon Acoustic Oscillations - I : Methods and Application to the Sloan Digital Sky Survey
• Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak
• Nonlinear Evolution of Baryon Acoustic Oscillations
• On the Robustness of the Acoustic Scale in the Low-Redshift Clustering of Matter
• Evolution of the cosmic web
• Bayesian physical reconstruction of initial conditions from large scale structure surveys
• nbodykit: an open-source, massively parallel toolkit for large-scale structure
• Power Spectrum Correlations Induced by Non-Linear Clustering
• The Halo Mass Function: High-Redshift Evolution and Universality
• Refined Second Law of Thermodynamics for fast random processes
• Cosmic flow from 2MASS redshift survey: The origin of CMB dipole and implications for LCDM cosmology
• Information field theory for cosmological perturbation reconstruction and non-linear signal analysis
• Reconstruction of the early Universe as a convex optimization problem
• Non-linear structure formation and the acoustic scale
• The Growth of Correlations in the Matter Power Spectrum
• A 2% Distance to z=0.35 by Reconstructing Baryon Acoustic Oscillations - II: Fitting Techniques
• High-precision predictions for the acoustic scale in the non-linear regime
• Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
• Action Principle Solutions For Galaxy Motions Within 3000 Km/s
• The Abacus Cosmos: A Suite of Cosmological N-body Simulations
• Iterative initial condition reconstruction
• A High-Fidelity Realization of the Euclid Code Comparison $N$-body Simulation with Abacus
• Lagrangian Dynamics in Non-Flat Universes and Non-Linear Gravitational Evolution
• Improving Initial Conditions for Cosmological $N$-Body Simulations
• On the least action principle in cosmology
• Reconstruction of cosmological density and velocity fields in the Lagrangian Zel'dovich Approximation
• Reconstruction of primordial density fields
• Rejuvenating Power Spectra II: the Gaussianized galaxy density field
• Reconstruction of cosmological initial conditions from galaxy redshift catalogues
• Peculiar Velocity Reconstruction with Fast Action Method: Tests on Mock Redshift Surveys
• The Cosmological Mean Density and its Local Variations Probed by Peculiar Velocities
• New method for initial density reconstruction
• Isobaric Reconstruction of the Baryonic Acoustic Oscillation
• Observational biases in Lagrangian reconstructions of cosmic velocity fields
• Reconstruction of the primordial Universe by a Monge--Ampere--Kantorovich optimisation scheme
• BAO reconstruction: a swift numerical action method for massive spectroscopic surveys
• Recovering the Primordial Density Fluctuations: A comparison of methods
• Reconstructing the spectrum of the pregalactic density field from astronomical data
• Bayesian cosmic density field inference from redshift space dark matter maps
• The Monge-Ampère-Kantorovich approach to reconstruction in cosmology
• Extended Fast Action Minimisation method: application to SDSS-DR12 Combined Sample
• A mechanical model for the transportation problem

Cited by in corpus (12)

• Sinkhorn Divergences for Unbalanced Optimal Transport
• Reconstruction of the neutrino mass as a function of redshift
• Reconstructing Cosmological Initial Conditions from Late-Time Structure with Convolutional Neural Networks
• Effective cosmic density field reconstruction with convolutional neural network
• Cosmological forecasts for future galaxy surveys with the linear point standard ruler: Toward consistent BAO analyses far from a fiducial cosmology
• Optimal Transport Reconstruction of Baryon Acoustic Oscillations
• Accurate Baryon Acoustic Oscillations reconstruction via semi-discrete optimal transport
• A new implementation of the geometric method for solving the Eady slice equations
• A unified derivation of Voronoi, power, and finite-element Lagrangian computational fluid dynamics
• Updated neutrino mass constraints from galaxy clustering and CMB lensing-galaxy cross-correlation measurements
• Higher-dimensional power diagrams for semi-discrete optimal transport
• Large-scale semi-discrete optimal transport with distributed Voronoi diagrams