An Introduction to Mathematical Cosmology 2nd Edition by J. N. Islam (PDF)

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 to 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 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐I picked this book up in the science library. Now I’m studying astrophysics. Get the picture?

⭐This book presents a review the basics of mathematical cosmology. For example a review of basic general relativity (a co-ordinate approach) is presented early on (Chapter 2). There are no exercises or problems. You could not learn general relativity from this.The discussion of the geometric and kinematic properties of the RW metric were good. Sufficient material is presented for reviews of standard cosmological models in chapters 3 and 5 although the material concerning the relativistic Friedmann models is covered much more clearly in Foster and Nightingale with the same end results and nice do-able exercises.. Chapter five presents a review of models with a cosmological constant.Some exact solutions (original work by the author) are presented. Rather frustratingly, solutions of some equations are presented with no hints at all as to how they are arrived at. Some approximate relationships are stated without suggesting how they are taken.This makes independent study of the book frustrating at times.There are two chapters later on that present the material from the mathematical supplement to Weinberg’s ‘three minutes’ book in more detail. These are quite fun and could be dipped into independently. I bought this book ‘hardback at paperback price – 14.95’ which was fair. I would not pay the full price for this book – save up and get Weinberg’s Gravitation and Cosmology or get it from the library. It is not really suitable for independent study.

⭐「数学的宇宙論」なる題名がついていますが、この本自身はそんなに数学的に書かれているわけではありません。入門ということなので、それでいいのかもしれませんが、もう少し分厚くてもよかったかなあと思います。内容はもちろん宇宙論ですが、構造形成とかいったそっち方面の話ではなく、アインシュタイン方程式の解としての宇宙論がメインみたいなので、そのあたりが確かに数学的なのかもしれません。相対論の標準的な教科書を勉強した後に読むといいかも。

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