الفهرس 
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Abstract
This thesis presents application of optimal control to the construction of some relativistic cosmological models: two standard models, and two inflationary models. Each model is formulated as an optimal control problem, which is then solved using optimal control techniques.
The thesis is organized into five chapters and a conclusion.
Chapter One starts with a brief history of ideas on the structure and origin of the universe. Then, Einstein’s theory of general relativity is outlined, and relativistic cosmology is introduced. The chapter ends with a review of optimal control theory and techniques.
Chapter Two presents a review of some standard cosmological models described by the solutions of Einstein’s field equations. The standard models are based on the Friedmann-Robertson-Walker metric.
Chapter Three presents the construction of two new standard cosmological models using optimal control.
- The first model is a closed universe with varying cosmological ”constant”. The model is constructed such that the universe has maximum life-time.
- The second model is a flat cosmological model with varying cosmological ”constant”.
The model is constructed such that the universe has maximum change of the cosmological ”constant”.
Chapter Four starts with a review of the problems facing standard cosmology near the big bang. Then, inflation is explained as a solution to those problems. Inflation postulates a period of accelerated expansion during the universe’s earliest stages. Some important inflationary models are reviewed.
Chapter Five introduces the construction of two new inflationary models using optimal control.
- The first model is a slow-roll inflationary model based on a self-interacting scalar field. The model is constructed such that the inflationary universe has minimum change of the scalar field.
- The second model is a flat inflationary model. The model is constructed such that the universe has minimum potential change.
The thesis concludes with a discussion of the results obtained, and suggestions for future work.
The work in this thesis is a good example of inter-disciplinary research. Problems in one field, relativistic cosmology, can be solved using methods and techniques of another field, optimal control.