An Introduction to Mathematical Cosmology

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Product Description

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.

An Introduction to Mathematical Cosmology Review

Some books on cosmology specialize in stating the concepts while keeping the mathematics to a minimum. Others state everything in more mathematical terms. Yet others are textbooks which get one to practice the mathematics. This book takes a different approach from any of these.

To understand cosmology, one needs to know some mathematics. And that would be true even if we knew all the answers to our questions. Given that there are actually multiple models of the universe that are being used and debated, it is even more important to see the mathematics that gets used to characterize them.

Still, this is not a textbook with problem sets. It is more of a review text in some areas (particularly general relativity), and a supplementary book in others. It addresses several important topics in cosmology in useful detail.

The book begins with an overview of cosmology and a review of general relativity. Then Islam spends a significant amount of time on the Robertson-Walker metric, with two different derivations of it. Next, we look at Friedman models of the universe. And then, we look at observational cosmology, with estimates and ranges for the Hubble constant and the resulting age of the universe (which hopefully comes out larger than the ages of the stars and galaxies).

After that, Islam discusses models with a cosmological constant. That's a good idea given that in the last few years, we have obtained more and more evidence for the existence of this (or of a dark energy term). He then includes an interesting chapter on singularities.

After this, there are chapters on the early universe. That means the temperature of the early universe and big bang nucleosynthesis. And we find out about the amounts of primordial helium and deuterium (I think these are still very intriguing issues). The author also shows us a variety of inflationary models (I had fun comparing this chapter with what Roger Penrose said about inflation in "The Road to Reality"). Islam then gives a brief account of quantum cosmology, including a mention of the Hartle-Hawking proposal for the wave function of the "ground state" of the universe.

The book concludes with a chapter about the distant future of the universe, including black hole evaporation and proton decay. While such a section may seem speculative and unsophisticated, I think such topics are a genuine part of cosmology.

This is a useful book, and I recommend it as a supplement to almost any cosmology text.

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