Nonlinear growth of perturbations in an Einstein-de Sitter cosmology

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1984

OSTI ID:5963855

Bertschinger, E W

Analytic and semi-analytic solutions for the nonlinear growth of perturbations in an Einstein-de Sitter universe are given. The first gives similarity solutions for the evolution of voids or holes. A negative density (or positive energy) perturbation grows until it becomes a hole, surrounded generally by a thin, dense shell. The shell and hole expand in a self-similar fashion. If there is no net mass deficit in the initial perturbation (i.e., the negative density perturbation is surrounded by a compensating overdense shell), the shell mass increases as t/sup (2/5)/. If there is a finite mass deficit, the shell mass increases as t/sup (2/3)/. Solutions valid asymptotically long after the initial perturbation becomes nonlinear are given for collisionless (e.g., massive neutrino), collisional (e.g., baryon), and mixed gases. In all of these solutions, shell-crossing and caustics occur in the collisionless component, while stocks form in the collisional fluid. Similarity solutions for secondary infall and accretion are given. A positive density perturbation decelerates faster than its surroundings and eventually turns around to recollapse. Since more distant mass shells are bound, they also turn arround, at successively later times for more distant shells. The evolution approaches a self-similar form, with the mass of accreted gas increasing as t/sup (2/3)/. Solutions are given for collisionless, collisional, and mixed fluids. Unless there is a central black hole, the density behaves in all components as p varies directly as ..sqrt../sup (9/4)/ for small r. The solutions lead therefore to nearly flat circular rotation curves, v/sub circ/ varies directly as ..sqrt../sup (1/8)/. Self-similar relaxation occurs in the collisionless fluid, with individual particle orbits becoming periodic after a few crossing times.

• OSTI ID: 5963855
• Country of Publication: United States
• Language: English

Related Subjects

640106* -- Astrophysics & Cosmology-- Cosmology
657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
COSMOLOGICAL MODELS
DE SITTER GROUP
EINSTEIN FIELD EQUATIONS
EQUATIONS
FIELD EQUATIONS
GALACTIC EVOLUTION
LIE GROUPS
MATHEMATICAL MODELS
SYMMETRY GROUPS