The Primordial Density Perturbation: Cosmology, Inflation and the Origin of Structure

`The beginning of the twenty-first century stands a good chance of being identified in history as the time when humankind first came to grips with the Universe . The emergence of the standard cosmological model had left by the wayside many concepts which in the late 1990s had still had possible relevance for our Universe'. Do these confident assertions by the authors of this new cosmology textbook show that we have reached an `end of history' regarding the big questions of cosmic origins, or is this just more in the line of Landau's quip: `Cosmologists are often in error, but never in doubt'? Despite Landau's comment having some justice at the time, a lot can change in science in over 50 years, and there is indeed a fair case that our overall picture of the Universe has converged. The standard cosmology is dominated by vacuum energy, and contains clumped dark matter whose inhomogeneity was seeded by quantum fluctuations during a period of `inflation', when the vacuum energy was very much higher than it is today. All the theoretical elements of this picture were put in place during a remarkable period of about three years at the start of the 1980s—a revolution surely comparable with the dawn of quantum mechanics in the 1920s. Consistency of this theory with observations hardened progressively during the 1990s, and all serious resistance finally evaporated in 2003 with the first detailed sky maps of the microwave background from NASA's WMAP satellite. The philosophy of this textbook is therefore a good one: rather than dwelling on how we arrived at our current understanding, the aim is to give a clear and clean presentation of the theory, preparing the interpretative framework for the new datasets that are set to arrive in the near future. This represents a deliberate departure from the broader perspective of the book written by the same authors (in the opposite order) in 2000: Lyth and Liddle's view is that the past decade has added so many new observations that the field has changed beyond the point where a simple update is sufficient, and it is hard to disagree. The benefits of the new approach show themselves in the elegance with which the book sets up the formalism for describing metric fluctuations in an expanding Universe, and how such fluctuations are generated during an early phase when the Universe is assumed to be dominated by the energy density of one or more hypothetical scalar fields. The key observables that let us probe this era are the scale-dependence of the density fluctuation spectrum; the tensor fluctuations (primordial gravity waves); and the extent to which the fluctuations deviate from a random-phase Gaussian character. Lyth in particular is an acknowledged master of this material, and has been responsible for creating significant parts of the formalism being described in the book. The fine details of calculating the origin of structure in exotic models are all present, and are set in the context of a nice pedagogical exposition and revision of relevant background in general relativity and field theory. This is a complete guide that can take a graduate student from undergraduate knowledge to calculations at the forefront of research. This book will thus be an indispensable companion for those researchers working in the theory of structure in the early Universe, and those teaching it at the postgraduate level. I have already found it useful for sharpening arguments in lecture notes that I previously regarded as fairly mature. It is not the only book in this area, but it is really the best on the fundamental topics where it concentrates its efforts. On the issue of computing the observational consequences of inflationary fluctuations (i.e. galaxy clustering and anisotropies in the Cosmic Microwave Background), Dodelson's Modern Cosmology (Academic Press) will probably have more appeal to most readers, simply because it treats these matters at greater length and with more use of physical analogy. But readers with some previous exposure to these topics will enjoy the stripped-down clarity of Lyth and Liddle's presentation. Dodelson also has the advantage that he gives outline solutions to his exercises, whereas Lyth and Liddle do not. I do think this is a pity, since students learn nothing from defeat by a problem they cannot solve, but can benefit enormously from struggling and then consulting a hint that helps them see where the key difficulty lay; something for the second edition, perhaps? In all of this, though, we should not lose sight of something a little peculiar. This is a textbook that provides great detail on a mature theory, which has seen great efforts and huge refinements over the past 30 years. And yet we have almost no idea if inflation is the correct theory of the early Universe. Some semi-popular treatments, even quite sophisticated ones, claim that observations of the CMB have proved inflation to be true, and one encounters many students who believe this excessive claim. The enthusiasm of advocates is understandable, since inflation has seen some great successes. Before it was suggested, we knew empirically that the early Universe must have had a mechanism for almost perfectly eliminating spatial curvature in the initial conditions, and generating fluctuations in an acausal manner, so that the Universe is very nearly uniform on large spatial scales, but not quite. The triumph of inflation is that it was designed to solve the first problem, and subsequently realized to offer in addition a possible solution to the second. But we really would like more direct evidence that the energy density was once dominated by a scalar field, and Lyth and Liddle's book is devoted to calculating the three observational signatures: `tilt' of the fluctuation spectrum, relic gravity waves, and non-Gaussianity. The first of these has already been seen, and if the other two signatures can be verified, then we would have a set of interlocking tests that could provide consistent verification of the theory. But as the authors admit in a coda, there are many models where these additional features will never be observable. Inflation would then remain in its current state: provisional acceptance by virtue of lack of an alternative. For the health of cosmology, we have to hope that future observations will be richer than this; as the data come in, Lyth and Liddle will be an essential guide.