Cosmology, Relativity, and Gravity Commons^™

Novel N-Body Orbits For Constrained Potentials Including The Unusual Figure Eight Three Body Orbit, Jan M. Dudzik

Masters Theses

Recently new n-body planar orbits have been discovered which are known as choreographies. These orbits correspond to small n, generally n<20, and exhibit unexpected patterns with respect to given initial conditions. Here we shall examine numerical solutions to the three-body problem and the restricted three-body problem for three body potentials that are the sum of three two-body potentials. Then for an everywhere attractive three body potential with non-collinear and collision-less orbits with a strictly monotone decreasing potential function there exist bound states that are not chaotic that are choreographies. For the right initial conditions these orbits can be mapped numerically and visualized. We will display a number of these cases corresponding to the three body problem, restricted three body problem, the chaotic restricted three body problem and the new figure eight bound state choreography for the Kazalov potential orbits to exhibit some of their special features and to take note of a number of open questions dealing with simple orbital problems.

Characterization Of Cosmic Microwave Background Temperature Fluctuations For Cosmological Topologies Specified By Topological Betti Numbers, Troy Gobble

Masters Theses

The cosmic microwave background explorer, COBE, and the Balloon Observations of Millimetric Extragalactic Radiation and Geophysics, BOOMERanG, have collected data from the universe and detected relic anisotropies indicative of one of the earliest events of the universe, decoupling. Hidden in the correlation between these temperature fluctuations is the signature of the global shape, or topology, of the early universe. It is possible to calculate the temperature fluctuations as due to primeval adiabatic density temperature fluctuations from the Sachs-Wolfe effect, which contains a topological term. Here we investigate some of the spaces and how they affect the microwave background.

A large …

Superstring Cosmology: An Investigation Into Low Temperature Effective Gauss-Bonnet Corrections To The Einstein Field Equations In An Inflationary Scenario, David Dressel

Masters Theses

Several problems with the inflationary cosmological model and the force coupling constants are addressed in the context of superstring theory. In order to simplify the field equations slightly, vacuum solutions are attempted. The solutions for several field equations are analyzed in order to obtain an inflationary universe that leads to a nearly static internal space. A solution is found when Gauss-Bonnet terms, as well as the Einstein terms, are used in the field equations, along with an exponential radii function for a ten dimensional product space. The solutions lead to a three-phase universe that might describe our very early universe. …