The Einstein Equations and the Large Scale Behavior of Gravitational Fields: 50 years of the Cauchy Problem in General Relativity

Cosmology is a discipline that encompasses many diverse aspects of physics and astronomy. This is part of its attraction, but also a reason why it is difficult for new researchers to acquire sufficient grounding to enable them to make significant contributions early in their careers. For this reason there are many cosmology textbooks aimed at the advanced undergraduate/beginning postgraduate level. Physical Foundations of Cosmology by Viatcheslav Mukhanov is a worthy new addition to this genre. Like most of its competitors it does not attempt to cover every single aspect of the subject but chooses a particular angle and tries to unify its treatment around that direction. Mukhanov has chosen to focus on the fundamental principles underlying modern cosmological research at the expense of some detail at the frontiers. The book places great emphasis on the particle-astrophysics interface and issues connected with the thermal history of the big-bang model. The treatment of big-bang nucleosynthesis is done in much more detail than in most texts at a similar level, for example. It also contains a very extended and insightful discussion of inflationary models. Mukhanov makes great use of approximate analytical arguments to develop physical intuition rather than concentrating on numerical approaches. The book is quite mathematical, but not in a pedantically formalistic way. There is much use of 'order-of-magnitude' dimensional arguments which undergraduate students often find difficult to get the hang of, but which they would do well to assimilate as early as possible in their research careers. The text is peppered with problems for the reader to solve, some straightforward and some exceedingly difficult. Solutions are not provided. The price to be paid for this foundational approach is that there is not much about observational cosmology in this book, and neither is there much about galaxy formation or large-scale structure. It also neglects some of the trendier recent developments in string-inspired cosmology, such as the braneworld scenario. Clearly one should cut one's teeth on standard fare before tackling a more exotic diet, but the lack of coverage of some of the most fashionable ideas may deter some potential readers. I would recommend this book to beginning graduate students intending to work on early Universe cosmology; it would be a good text for Masters level courses for physics students entering this area too. It is probably a bit too intense for physics undergraduate courses at a lower level than this in British universities. On the other hand, Mukhanov does such a good job at deconstructing well-established aspects of the big bang that I found much of interest myself. I suspect it will find its way onto the bookshelves of research physicists at all levels. (book review)