Reconstruction of the early Universe as a convex optimization problem

@article{Brenier2003ReconstructionOT,
  title={Reconstruction of the early Universe as a convex optimization problem},
  author={Yann Brenier and Uriel Frisch and Michel H{\'e}non and Gr{\'e}goire Loeper and S. Matarrese and Roya Mohayaee and Andrei Sobolevskii},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={2003},
  volume={346},
  pages={501-524}
}
We show that the deterministic past history of the Universe can be uniquely reconstructed from knowledge of the present mass density field, the latter being inferred from the three-dimensional distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales – a few Mpc – where multistreaming becomes significant. Above 6 h−1 Mpc we propose and implement an effective Monge–Ampere–Kantorovich method of… Expand
A fast semi-discrete optimal transport algorithm for a unique reconstruction of the early Universe
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 onExpand
New method for initial density reconstruction
A theoretically interesting and practically important question in cosmology is the reconstruction of the initial density distribution provided a late-time density field. This is a long-standingExpand
O ct 2 00 4 Reconstruction of large-scale peculiar velocity fields
A reconstruction method for recovering the initial conditions of the Universe starting from the present galaxy distribution is presented which guarantees uniqueness of solutions. We show how ourExpand
Reconstructing the baryon acoustic oscillations using biased tracers.
The reconstruction of the initial conditions of the Universe is an important topic in cosmology, particularly in the context of sharpening the measurement of the baryon acoustic oscillation (BAO)Expand
ELUCID -- Exploring the Local Universe with the reConstructed Initial Density field. II: Reconstruction diagnostics, applied to numerical halo catalogs
The ELUCID project aims to build a series of realistic cosmological simulations that reproduce the spatial and mass distribution of the galaxies as observed in the Sloan Digital Sky Survey (SDSS).Expand
Reconstruction of primordial density fields
The Monge–Ampere–Kantorovich (MAK) reconstruction is tested against cosmological N-body simulations. Using only the present mass distribution sampled with particles, and the assumption of homogeneityExpand
Reconstructing cosmological initial conditions from galaxy peculiar velocities – I. Reverse Zeldovich Approximation
We propose a new method to recover the cosmological initial conditions of the presently observed galaxy distribution, which can serve to run constrained simulations of the Local Universe. Our method,Expand
Optimal transport by omni-potential flow and cosmological reconstruction
One of the simplest models used in studying the dynamics of large-scale structure in cosmology, known as the Zeldovich approximation, is equivalent to the three-dimensional inviscid Burgers equationExpand
The Monge-Ampère-Kantorovich approach to reconstruction in cosmology
Motion of a continuous fluid can be decomposed into an "incompressible" rearrangement, which preserves the volume of each infinitesimal fluid element, and a gradient map that transfers fluid elementsExpand
Bayesian cosmic density field inference from redshift space dark matter maps.
TLDR
Novel algorithmic implementations are introduced regarding the mass assignment kernels when defining the dark matter density field and optimization of the time-step in the Hamiltonian equations of motions and the resulting reconstructed fields are isotropic and their power spectra are unbiased compared to the true field defined by the authors' mock observations. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 83 REFERENCES
A reconstruction of the initial conditions of the Universe by optimal mass transportation
TLDR
This work shows that reconstruction can be reduced to a well-determined problem of optimization, and presents a specific algorithm that provides excellent agreement when tested against data from N-body simulations. Expand
RECONSTRUCTION OF COSMOLOGICAL INITIAL CONDITIONS FROM GALAXY REDSHIFT CATALOGUES
We present and test a new method for the reconstruction of cosmological initial conditions from a full-sky galaxy catalogue. This method, called ZTRACE, is based on a self-consistent solution of theExpand
An improved reconstruction method for cosmological density fields
This paper proposes some improvements to existing reconstruction methods for recovering the initial linear density and velocity fields of the universe from the present large-scale densityExpand
Back to the primordial Universe by a Monge-Ampère-Kantorovich optimization scheme
A new method for reconstruction of the primordial density fluctuation field is presented. Various previous approaches to this problem rendered non-unique solutions. Here, it is demonstrated that theExpand
Simulating Our Cosmological Neighborhood: Mock Catalogs for Velocity Analysis
We describe the construction of an N-body simulation that mimics the true velocity and mass-density fields in a box of side 256\hmpc about the Local Group , and the production of mock catalogs thatExpand
Recovering the Primordial Density Fluctuations : A comparison of methods
We present a comparative study of different methods for reversing the gravitational evolution of a cosmological density field to recover the primordial fluctuations. We test six different approximateExpand
Peculiar velocity reconstruction with the fast action method: tests on mock redshift surveys
We present extensive tests of the fast action method (FAM) for recovering the past orbits of mass tracers in an expanding universe from their redshift-space coordinates at the present epoch. TheExpand
On the least action principle in cosmology
Given the present distribution of mass tracing objects in an expanding universe, we develop and test a fast method for recovering their past orbits using the least action principle. In this method,Expand
Reconstruction analysis of galaxy redshift surveys: a hybrid reconstruction method
In reconstruction analysis of a galaxy redshift survey, one works backward from the observed galaxy distribution to the primordial density field in the same region of space, then evolves theExpand
Large scale structure of the universe and cosmological perturbation theory
Abstract We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitationalExpand
...
1
2
3
4
5
...