Mathematics – Logic
Scientific paper
Apr 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007cqgra..24r1895.&link_type=abstract
Classical and Quantum Gravity, Volume 24, Issue 7, pp. 1895-1896 (2007).
Mathematics
Logic
Scientific paper
The award of the 2006 Nobel Prize for Physics is a reminder to non-specialists that the cosmic microwave background (CMB) has yielded astonishing advances in our understanding of cosmology. Mather and Smoot received their prize for work done with NASA's COBE satellite in the early 1990s, but the subject has if anything accelerated since then. The results from NASA's WMAP satellite, reported in 2003 and 2006, have proved COBE's equal in importance and have generated huge worldwide interest. There could therefore hardly be a better time to be writing a detailed textbook to explain what the fuss is all about to a new generation of research students.
A comprehensive treatment of the physics of the CMB is not easy to achieve, because it is connected to so much else in cosmology. A student must have a background knowledge of the geometry and dynamics of an expanding universe, plus a deep exposure to the physics of quantum fields, in order to understand the modern `inflationary' view in which the universe was set expanding by the tension of the vacuum, and was seeded with small inhomogeneities as a result of quantum fluctuations.
Although the theory of inflation is not yet verified, the CMB has the potential to accomplish this; testing inflation is undoubtedly one of the principal aims of cosmology over the next decade. Even with this preparation, understanding the properties of the CMB is quite hard at the professional level, requiring the perturbation expansion of the relativistic Boltzmann equation. These technical difficulties are particularly strong in the frontier area of CMB polarization.
Naselsky and his collaborators have allocated themselves a relatively brief 255 pages in which to meet these challenges, so some compromise is inevitable. Although the preface is not explicit about the assumed prior knowledge, no systematic material on background cosmology or on inflation is to be found. The former is reasonable in a graduate-level text (which this certainly is), but the latter is surprising in the context of a subject whose whole purpose is to observe the properties of primordial perturbations that may have arisen from inflation.
Instead, the text concentrates on the technical heartland of the transport theory for CMB photons, and the Newtonian and relativistic theory for the development of CMB anisotropies, including polarization. It closes with more observationally-based chapters on general statistical aspects of the CMB sky, a digest of the recent results from WMAP, and an outlook. These are welcome, but the book really stands or falls on its treatment of the core physics of anisotropies.
Without going too much into specifics, it can be fairly stated that the treatment given of the main material on CMB fluctuations is geared more to working professionals than to students. There is a good deal of useful technical detail, but it is not always derived systematically, and sometimes arises by reference to the research literature. There are no problem sets or worked examples, and not much attempt at intuitive illumination. As an example, one might point to the large-angle anisotropies of the CMB, which were first analysed in the classic Sachs Wolfe paper of 1967. The relativistic transport equation is there, but one looks in vain for the separation into the Sachs Wolfe effect proper (potential perturbations at last scattering) and the integrated effect of evolution since then. This latter ISW effect is in fact of huge interest in current research, since it is one of the methods for probing whether the vacuum energy differs from a cosmological constant. In general, the text seems strangely patchy on issues of contemporary interest, certainly in terms of its emphasis. It is as if the three authors contributed material separately without achieving a full integration.
On the more positive side, the book has the advantage that it presents a Russian view of the subject. So much of the initial work on the `Relic Radiation' (a much better name for the CMB) was done in Russia, and it is good to see these early authors receive the credit they deserve. But these historical advantages cannot obscure the fact that good books already exist on this subject, whereas the present text does not feel all that carefully thought through.
One reflection of this may be found in the index: at only two pages, this is far too short to be useful—and it doesn't help that all the page numbers I tried to look up were incorrect. In contrast, the cosmology texts by Dodelson and by Mukhanov, for example, seem to me to be more consistent in their level and clearer in their pedagogical approach. They find a better balance between formalism and insight, and have ample problem material to help the reader progress.
These texts are good recommendations for advanced students; the present book contains much useful information, but will appeal most to those who already know the subject well.
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