
Contents
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6. Newtonian Approximation 6. Newtonian Approximation
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7. Particle Dynamics in Expanding Coordinates 7. Particle Dynamics in Expanding Coordinates
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8. The Peculiar Acceleration 8. The Peculiar Acceleration
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9. Two Models; The Vlasov Equation and the Ideal Fluid 9. Two Models; The Vlasov Equation and the Ideal Fluid
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A. Vlasov equation A. Vlasov equation
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B. Ideal fluid B. Ideal fluid
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10. Linear Perturbation Approximation for δ 10. Linear Perturbation Approximation for δ
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11. Solutions for δ(t): p = Λ = 0 11. Solutions for δ(t): p = Λ = 0
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A. Einstein-de sitter model A. Einstein-de sitter model
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B. Open model B. Open model
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C. Closed model C. Closed model
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12. Solutions for δ(t): Effect of a Uniform Radiation Background 12. Solutions for δ(t): Effect of a Uniform Radiation Background
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13. Solutions for δ(t): Models with Λ ≠ 0 13. Solutions for δ(t): Models with Λ ≠ 0
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14. The Peculiar Velocity Field 14. The Peculiar Velocity Field
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15. Joining Conditions for δ and v 15. Joining Conditions for δ and v
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16. Critical Jeans Length 16. Critical Jeans Length
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17. Primeval Magnetic Field as a Source for δρ/ρ 17. Primeval Magnetic Field as a Source for δρ/ρ
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18. Second Order Perturbation Theory for δρ/ρ 18. Second Order Perturbation Theory for δρ/ρ
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19. Spherical Model 19. Spherical Model
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A. Energy and maximum radius A. Energy and maximum radius
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B. Motion of a mass shell B. Motion of a mass shell
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C. The density run C. The density run
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D. Behavior in the limit Ω → 0 D. Behavior in the limit Ω → 0
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E. Closed and flat cosmological models E. Closed and flat cosmological models
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20. Homogeneous Ellipsoid Model 20. Homogeneous Ellipsoid Model
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21. Caustics and Pancakes 21. Caustics and Pancakes
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A. General treatment A. General treatment
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B. Kinematic approximation B. Kinematic approximation
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C. Remarks C. Remarks
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22. Expansion, Vorticity, and Shear 22. Expansion, Vorticity, and Shear
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23. Origin of the Rotation of Galaxies 23. Origin of the Rotation of Galaxies
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24. Cosmic Energy Equation 24. Cosmic Energy Equation
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A. Free particle model A. Free particle model
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B. Ideal fluid model B. Ideal fluid model
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25. Spherical Accretion Model 25. Spherical Accretion Model
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26. Hierarchical Clustering Model 26. Hierarchical Clustering Model
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27. Fourier Transform of the Equations of Motion 27. Fourier Transform of the Equations of Motion
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28. Coupling of Density Fluctuations 28. Coupling of Density Fluctuations
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A. Miminal fluctuations A. Miminal fluctuations
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B. k4 Spectrum from gravity dynamics B. k4 Spectrum from gravity dynamics
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C. Cancellation of nonlinear effects from stable clusters C. Cancellation of nonlinear effects from stable clusters
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D. Model for newly forming clusters D. Model for newly forming clusters
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E. Summary E. Summary
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II. Behavior of Irregularities in the Distribution of Matter: Newtonian Approximation
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Published:September 2020
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Abstract
This chapter examines the behavior of a given mass distribution in the Newtonian approximation. Discussion of how irregularities in the matter distribution behave in an expanding universe is greatly simplified by the fact that a limiting approximation of general relativity, Newtonian mechanics, applies in a region small compared to the Hubble length. The rest of the universe can affect the region only through a tidal field. Though the point was clearly made by Georges Lemaître, it has not always been recognized that the Newtonian approximation is not a model but a limiting case valid no matter what is happening in the distant parts of the universe. Because of the importance of this result, the chapter discusses it at some length.
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