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  How smooth are particle trajectories in a Lambda CDM Universe?

Rampf, C., Villone, B., & Frisch, U. (2015). How smooth are particle trajectories in a Lambda CDM Universe? Monthly Notices of the Royal Astronomical Society, 452(2), 1421-1436. doi:10.1093/mnras/stv1365.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0026-BBEC-3 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-9A8A-5
Genre: Journal Article

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 Creators:
Rampf, Cornelius1, Author
Villone, Barbara, Author
Frisch, Uriel, Author
Affiliations:
1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24008              

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Free keywords: Astrophysics, Cosmology and Extragalactic Astrophysics, astro-ph.CO,General Relativity and Quantum Cosmology, gr-qc
 Abstract: Very. Indeed, it is shown here that in a flat, cold dark matter (CDM) dominated Universe with positive cosmological constant ($\Lambda$), modelled in terms of a Newtonian and collisionless fluid, particle trajectories are analytical in time (representable by a convergent Taylor series) until at least a finite time after decoupling. The time variable used for this statement is the cosmic scale factor, i.e., the "$a$-time", and not the cosmic time. For this, a Lagrangian-coordinates formulation of the Euler-Poisson equations is employed, originally used by Cauchy for 3-D incompressible flow. Temporal analyticity for $\Lambda$CDM is found to be a consequence of novel explicit all-order recursion relations for the $a$-time Taylor coefficients of the Lagrangian displacement field, from which we derive the convergence of the $a$-time Taylor series. A lower bound for the $a$-time where analyticity is guaranteed and shell-crossing is ruled out is obtained, whose value depends only on $\Lambda$ and on the initial spatial smoothness of the density field. The largest time interval is achieved when $\Lambda$ vanishes, i.e., for an Einstein-de Sitter universe. Analyticity holds also if, instead of the $a$-time, one uses the linear structure growth $D$-time, but no simple recursion relations are then obtained. The analyticity result also holds when a curvature term is included in the Friedmann equation for the background, but inclusion of a radiation term arising from the primordial era spoils analyticity.

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 Dates: 2015-03-282015
 Publication Status: Published in print
 Pages: 16 pages, 4 figures, to be submitted to MNRAS
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1504.00032
DOI: 10.1093/mnras/stv1365
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Title: Monthly Notices of the Royal Astronomical Society
  Other : Mon. Not. R. Astron. Soc.
Source Genre: Journal
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Publ. Info: Oxford : Oxford University Press
Pages: - Volume / Issue: 452 (2) Sequence Number: - Start / End Page: 1421 - 1436 Identifier: ISSN: 1365-8711
CoNE: /journals/resource/1000000000024150