The Cosmic Microwave Background ,

A Primer on the Physics of the Cosmic Microwave Background ,

The cosmic microwave background is relic radiation emitted about 300 000 years after the Big Bang, when the universe was only about 1/1000 of its present size. At that time, light and matter decoupled and light began to permeate space, traveling in all directions more or less unobstructed. The 1965 discovery of the CMB was commemorated by the Nobel Prize awarded in 1978 to Arno Penzias and Robert Wilson.

That discovery was followed by intense experimental and theoretical effort that unraveled two important features of the CMB. First, its spectrum is the most perfect blackbody spectrum known and corresponds to a temperature of about 2.7 K. Second, the CMB, although very uniform, is not perfectly so. It has small temperature fluctuations of roughly one part in 100 000 that encode information about the distribution of matter in the universe at the time the CMB was emitted. The discoveries of those two features yielded a second Nobel Prize for CMB work—to George Smoot and John Mather in 2006.

Today, the CMB is one of cosmology’s most important objects of study. Its potency lies in that the fluctuations in the early universe were small and therefore can be fully treated by perturbation theory. The theory, however, is not for the light-hearted; understanding it thoroughly requires a good grasp of general relativity, statistical mechanics, and quantum field theory on curved space-times. And only recently has CMB analysis reached the level of maturity that warrants writing textbooks entirely dedicated to the subject. Ruth Durrer’s *The Cosmic Microwave Background * and Massimo Giovannini’s *A Primer on the Physics of the Cosmic Microwave Background * are two important attempts to present the complete theory behind the CMB in a self-contained manner—including the gory details that are often skipped or simplified in other books. They are not best suited for those who are first diving into cosmology; instead they are geared toward graduate students specializing in the CMB or related fields, or to practicing researchers, for whom they can serve as standard references.

The two books have much in common. To start, both are authored by undisputed masters in the field. Ruth Durrer, professor of theoretical physics at the University of Geneva, has done foundational work on cosmological perturbation theory and alternative models of the early universe. Massimo Giovannini, of the Enrico Fermi Center and CERN, has worked on notoriously difficult problems such as understanding magnetic fields in the early universe. Both books contain the obligatory material, including an overview of the standard homogeneous model and of the thermodynamics and statistical mechanics of the early universe, and both carefully develop perturbation theory around the background metric. Durrer’s book is a little shorter, and I find it more pedagogical and better organized. She develops a gauge-invariant formulation of the theory, which is more elegant but requires somewhat more work than other approaches. Giovannini, on the other hand, works with both gauge-dependent and gauge-invariant formulations and has a particularly amusing chapter on “surfing on the gauges.” His extended treatment is particularly useful for those who will need to plow through massive amounts of published literature. Both authors discuss polarization of the CMB, but whereas Durrer devotes an entire chapter to the subject, Giovannini essentially develops the necessary analytic tools in the course of his discussion of intensity perturbations.

The texts also have important differences in focus. Durrer delves further into lensing of the CMB and the statistical methods used for parameter estimation, and she includes a full chapter on the deviations of the CMB spectrum from the black-body form. Conversely, Giovannini discusses several technical aspects of numerical CMB computation—for example, the tight-coupling approximation—and he gives a fuller introduction to various theories of inflation.

Although the union of topics discussed in the two books is extensive, I still find subjects that I wish were covered. Those include the integrated Sachs–Wolfe effect and its measurement through cross correlation with tracers of matter, primordial non-Gaussianity and the bispectrum it induces, and issues associated with patchy reionization. I would have also liked to read more discussion of, among other things, the recombination process and the Sunyaev–Zeldovich effect and its impact on the power spectrum. Given that Durrer has worked extensively on noninflationary sources of cosmic structure, such as topological defects and scaling seeds, the subject deserves to have a full chapter to itself in her book rather than being crammed into a section in a chapter on parameter estimation.

Both books are important additions to a cosmologist’s library. Durrer’s book is a distillation of years of development of CMB theory into a single coherent and unified story. It links theory and observations and teaches how to connect the two to learn about the universe. Giovannini’s book, in contrast, is anchored in the inflationary model of the universe and illustrates the important link between the theory of inflation and the theory of CMB fluctuations. More importantly, the formalism in Giovannini’s book, although perhaps less elegant, yields equations that are closer to those used in standard numerical codes. The two books are complementary, and graduate advisers should have both of them ready to hand out to their graduate students as the need arises. I will definitely keep both books on my shelf.