Elements of String Cosmology , Maurizio Gasperini , Cambridge U. Press, New York, 2007. $85.00 (552 pp.). ISBN 978-0-521-86875-4
One of the most important ongoing challenges in theoretical physics is to understand the nature of the Big Bang that started our universe. Albert Einstein’s general theory of relativity, the best classical theory of gravity, predicts that the Big Bang is a singularity in which the density of matter and the curvature of spacetime both become infinite. General relativity, however, must break down before such singularities can form because quantum effects will become important. The physics near the Big Bang is thus a problem in quantum gravity.
String theory is the most actively studied approach to quantum gravity, and using it to try to determine the physics of the early universe is only natural. Maurizio Gasperini’s Elements of String Cosmology is a good introduction to that active area of research. Gasperini, a professor of theoretical physics at the University of Bari in Italy, is a recognized expert in string cosmology and one of the inventors of the pre–Big Bang model (which is described later in the review). There are several excellent books on string theory, such as the two-volume String Theory (Cambridge University Press, 1998) by Joseph Polchinski (see the review in Physics Today, Physics Today 0031-9228 52 6 1999 59 https://doi.org/10.1063/1.882705 June 1999, page 59 ) and String Theory and M-Theory: A Modern Introduction (Cambridge University Press, 2007) by Katrin Becker, Melanie Becker, and John Schwarz (see the review in Physics Today, Physics Today 0031-9228 61 5 2008 57 https://doi.org/10.1063/1.2930740 May 2008, page 57 ). But unlike those texts, Gasperini’s is dedicated to string cosmology. The book is intended for graduate students who have a background in general relativity and quantum field theory, but not necessarily in string theory or cosmology.
Gasperini’s book has many attractive features. Its cosmology side offers a good introduction to inflationary cosmology and an extensive discussion of scalar and tensor perturbations—potentially observable signatures that might be used to distinguish models of the early universe. The string-theory side presents good discussions of the low-energy effective action of string theory, homogeneous and anisotropic solutions to the theory, T-duality symmetries, and the physics of the dilaton. The author even includes the first-order higher-derivative corrections from bosonic and heterotic string theory. Most calculations are carried out in detail to make it easy for students to follow.
Despite the enormous progress in string theory, experts have reached no consensus about what it predicts for the early universe. A large part of the book is devoted to the pre–Big Bang scenario. That model posits an early collapsing phase of our universe before the Big Bang and assumes that the Big Bang was really a “big bounce.” Gasperini makes clear in the preface that he does not intend to provide a comprehensive review of all the work in string cosmology, but even so, I found the focus on the pre–Big Bang scenario to be excessive for “the first book dedicated to string cosmology,” as mentioned on the back cover. For example, the popular and extensively studied brane-world models are only discussed in the final chapter.
A few other things bothered me about the book. Including the first-order string corrections makes the equations of motion much more complicated, and it is not clear how much one learns for the extra effort. Typically, when the first correction becomes important, all the higher-order corrections, which have not been included, also become significant, and one loses control of the calculation. Moreover, the book does not include any problems for the student, so it is not ideal as a textbook. Most of the chapters include appendixes that the author claims are self-contained discussions of special topics. However, chapter 4 begins by referring frequently to the equations in the 40-page appendix to chapter 3, which discusses the quantization of the free bosonic and supersymmetric strings.
Despite such shortcomings, Elements of String Cosmology is an excellent resource for the graduate student interested in learning string cosmology, especially the pre–Big Bang scenario. The text provides a clear explanation of the results of hundreds of research articles. Thus it is a good starting point for those entering this exciting field.
