Mathematics – Logic
Scientific paper
May 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007cqgra..24.2443.&link_type=abstract
Classical and Quantum Gravity, Volume 24, Issue 9, pp. 2443-2444 (2007).
Mathematics
Logic
Scientific paper
Here are two textbooks, both published by Springer and each roughly half devoted to cosmology—the large scale structure and evolution of the Universe. I can imagine a context (not the same context) in which each would be useful. And there the similarities largely end. Bergstrom and Goobar's (hereafter B&G) other topic is particle astrophysics, and they are addressing students who already have some knowledge of advanced quantum mechanics and classical field theory (or who can master some relativistic dynamics and the Dirac equation on the basis of a couple of very information-dense appendices). The book is meant for use at the graduate level, probably the second year by US standards (the authors are from Stockholm).
Schneider (hereafter PS), on the other hand, begins with galaxies, and then alternates between cosmological topics of gradually increasing sophistication (expanding universe to CMB fluctuations) and additional galactic topics—clusters, quasars and all. The book is meant as the second half of an introductory astronomy/astrophysics course for physics majors, and in the US would fit into an upper division `capstone' course.
Each is meant for a single semester class at the target level, and might be squeezed into a 10-week term with elimination of some topics. B&G is a paperback of a second edition, with colour confined to a central block of plates, relatively few graphs and drawings, but lots of complex equations. PS is a hard cover translation from a German original, with colour used freely in astronomical images and graphs throughout, with fewer and less complex equations. Though the nominal difference in copyright date is only two years (2006 for PS, 2004 for B&G), the former is considerably more up to date, mentioning, for instance, that the third year WMAP results are not different enough from the first year to justify redoing drawings and such (I agree).
What can you expect to get if you buy one or both of these? B&G have a homepage of error corrections. There are worked problems in the text and 2-15 problems at the ends of each of the 15 chapters (5 on average). I can do at least some of them. The list of references or suggestions for further reading is partly out of date and gives no indication of the levels of the books mentioned. The preface promises a list of outstanding texts in particle physics and cosmology to appear at the end of the first chapter. Either this is the (rather unsatisfactory) list at the end of the book, or it has disappeared completely. The reader is also referred to the arXiv astro-ph and hep-ph sections and to proceedings of the Texas and TAUP conference series for current information. Some, but not all, of the equations and problems choose c = G = 1 or c = planck = 1 units. The discussion of inflation includes flatness, horizon and monopole problems, but not the production and amplitude of primordial fluctuations.
The PS appendices are very basic astronomy, and the units are generally cgs and astronomical (but with a sudden outbreak of light years in one place). The text and author do not have their own website, but readers are referred to both arXiv and ADS. The description of histories of current issues is sometimes superficial (but so is that of B&G). The basic equations relating H, ρ, Λ and others are in the optimal form for actually estimating numerical values (which is less true of B&G). There are particularly good quantitative treatments of gravitational lensing (the author's speciality) and basic cosmological models. Other topics, like active galaxies, are presented attractively but qualitatively, and one might be hard pressed to come up with suitable homework and exam problems covering them. There are some classic `back of the envelope' calculations embedded in the text, but no problems at the ends of the chapters. The treatment of inflation mentions only the flatness and horizon problems, and it may take you a while to find the bits you want. The index lists neither lambda nor the cosmological constant, and inflation is said to appear on pp 307-412. The chapters are of equal length, in traditional textbook fashion.
Neither volume has much to say about issues that are currently `hot'—the importance of extra dimensions, fine tuning of cosmological parameters, possible evidence for cosmic geometry different from the simplest. Discussions of such things will, of course, date a textbook quickly. On the other hand, they are often the items that physics (etc) students will have heard about in colloquia and would like to have clarified. Names appear only as eponyms, from Altarelli Parisi evolution (which is not on the page to which B&G's index refers you) to the Zeeman effect, which is where PS's index says it is.
Can I imagine using either of these as texts? Definitely yes for PS, since it is a possible fit to an astrophysics course that UCI offers as a `vocabulary builder' for students coming out of mainstream physics (and for which we have yet to find an entirely suitable text). We are contemplating a faculty hire or two in astro-particle physics, in which case B&G might well be a good fit to a seminar for students beginning work in that area. If I were asked to teach the course, however, I would probably want an instructor's solution manual for the text problems. One may well exist, though the book does not mention it. Using PS, you will have to make up your own problems (which you can then reasonably be expected to be able to work without help).
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