Cosmology in one dimension: A two-component model

Shiozawa, Yui; Miller, Bruce N.

doi:10.1016/j.chaos.2016.05.008

Cited by 4 publications

(2 citation statements)

References 24 publications

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“…Further, the expected slopes for long (P ∼ k) and short (P ∼ k −3 ) wavelengths are correctly recovered by the Dirac-Milne simulations. This power law behavior in the nonlinear regime suggests a self-similar matter distribution in each model, pointing to the existence of a robust fractal dimension [21,31].…”

Section: Simulation Resultsmentioning

confidence: 80%

Structure formation in a Dirac-Milne universe: Comparison with the standard cosmological model

et al. 2020

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Simulation Resultsmentioning

confidence: 80%

Structure formation in a Dirac-Milne universe: Comparison with the standard cosmological model

et al. 2020

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“…More recent studies (see, for example, Miller & Rouet, 2010;Joyce & Sicard, 2011;Benhaiem et al, 2013) have shown that power spectrum of initial perturbations in 1D models leads to fractal and multifractal structures in a wide range of scales. Detailed review of the problem can be found in Shiozawa & Miller (2016). Onedimensional cosmological models seem to give correct qualitative understanding of many events in the gravitational collapse of three-dimensional universe, but some ambiguity still remains as to how to connect the properties of 1D and 3D models (Joyce & Sicard, 2011).…”

Section: Introductionmentioning

confidence: 99%

Kinetic properties of fractal stellar media

Chumak

Rastorguev

2016

Mon. Not. R. Astron. Soc.

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Kinetic processes in fractal stellar media are analysed in terms of the approach developed in our earlier paper (Chumak & Rastorguev, 2015) involving a generalization of the nearest neighbour and random force distributions to fractal media. Diffusion is investigated in the approximation of scale-dependent conditional density based on an analysis of the solutions of the corresponding Langevin equations. It is shown that kinetic parameters (time scales, coefficients of dynamic friction, diffusion, etc.) for fractal stellar media can differ significantly both qualitatively and quantitatively from the corresponding parameters for a quasi-uniform random media with limited fluctuations. The most important difference is that in the fractal case kinetic parameters depend on spatial scale length and fractal dimension of the medium studied. A generalized kinetic equation for stellar media (fundamental equation of stellar dynamics) is derived in the Fokker-Planck approximation with the allowance for the fractal properties of the spatial stellar density distribution. Also derived are its limit forms that can be used to describe small departures of fractal gravitating medium from equilibrium.

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From chaos to cosmology: insights gained from 1D gravity

Miller

Manfredi

Pirjol

et al. 2023

Class. Quantum Grav.

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The gravitational force controls the evolution of the universe on several scales. It is responsible for the formation of galaxies from the primordial matter distribution and the formation of planets from solar nebulae. Because the gravitational force is singular and has infinite range, making predictions based on fully three-dimensional models may be challenging. One-dimensional (1D) Newtonian gravity models were proposed as toy models for understanding the dynamics of gravitational systems. They can be integrated exactly and were used for computer simulations starting in the 1960s, providing the first demonstration of violent relaxation and the rapid development of long-lived quasi-stationary states. The present review provides the bases of the physics of 1D gravitational systems. It is divided into two main parts, the first concerning the approach to equilibrium and the second applications to cosmology. Each part is self-contained and can be read independently of the other. In the first part, we provide an introduction to the equilibrium thermodynamics of the one-dimensional gravitational sheet (OGS) system in the Vlasov limit. Both fixed and periodic boundary conditions are considered. The relaxation to equilibrium of the OGS is studied through numerical simulations which establish the role played by quasi-stationary states and violent relaxation. We also survey existing work on the Lyapunov exponents of the OGS and on the chaotic dynamics of 1D systems with few particles, focusing on the 1D three-body problem. The second part summarizes work on dynamical structure formation in cosmology using 1D systems. By transforming to comoving coordinates, which follow the global expansion of the universe, the 1D approach provides a useful laboratory for studying structure formation in various cosmological scenarios, from Einstein-de Sitter and $\Lambda$CDM to more recent, alternative cosmological models. A key result is the appearance of scale-free behavior with fractal dimension, which can be reliably studied in 1D for large systems over many epochs. Finally, an appendix gives some details on the numerical simulation methods used in these studies.

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Cosmology in one dimension: A two-component model

Cited by 4 publications

References 24 publications

Structure formation in a Dirac-Milne universe: Comparison with the standard cosmological model

Structure formation in a Dirac-Milne universe: Comparison with the standard cosmological model

Kinetic properties of fractal stellar media

From chaos to cosmology: insights gained from 1D gravity

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