An Introduction to Mathematical Cosmology

by J. N. Islam

• ISBN13: 9780521496506
• ISBN10: 0521496500
• eBook ISBN(s): 9780511037931
• Edition: 2nd
• Format: Hardcover
• Copyright: 2001-12-17
• Publisher: Cambridge University Press

Summary

This book provides a concise introduction to the mathematical aspects of the origin, structure and evolution of the universe. The book begins with a brief overview of observational and theoretical cosmology, along with a short introduction of general relativity. It then goes on to discuss Friedmann models, the Hubble constant and deceleration parameter, singularities, the early universe, inflation, quantum cosmology and the distant future of the universe. This new edition contains a rigorous derivation of the Robertson-Walker metric. It also discusses the limits to the parameter space through various theoretical and observational constraints, and presents a new inflationary solution for a sixth degree potential. This book is suitable as a textbook for advanced undergraduates and beginning graduate students. It will also be of interest to cosmologists, astrophysicists, applied mathematicians and mathematical physicists.

Table of Contents

Preface to the first edition	ix
Preface to the second edition	xi
Some basic concepts and an overview of cosmology	1	(11)
Introduction to general relativity	12	(25)
Summary of general relativity	12	(6)
Some special topics in general relativity	18	(19)
Killing vectors	18	(3)
Tensor densities	21	(3)
Gauss and Stokes theorems	24	(4)
The action principle for gravitation	28	(4)
Some further topics	32	(5)
The Robertson-Walker metric	37	(23)
A simple derivation of the Robertson-Walker metric	37	(5)
Some geometric properties of the Robertson-Walker metric	42	(3)
Some kinematic properties of the Robertson-Walker metric	45	(6)
The Einstein equations for the Robertson-Walker metric	51	(2)
Rigorous derivation of the Robertson-Walker metric	53	(7)
The Friedmann models	60	(8)
Introduction	60	(4)
Exact solution for zero pressure	64	(3)
Solution for pure radiation	67	(1)
Behaviour near t = 0	68	(1)
Exact solution connecting radiation and matter eras	68