### Welcome to the Universe

*by Neil deGrasse Tyson, Michael A Strauss and J Richard Gott*

**Princeton University Press**

It is commonly believed that popular-science books should abstain as much as possible from using equations, apart from the most iconic ones, such as E = mc^{2}. The three authors of *Welcome to the Universe* boldly defy this stereotype in a book that is intended to guide readers with no previous scientific education from the very basics (the first chapters explain the scientific notation, how to round-up numbers and some trigonometry) to cutting-edge research in astrophysics and cosmology.

This book reflects the content of a course that the authors gave for a decade to non-science majors at Princeton University. They are a small dream team of teachers and authors: Tyson is a star of astrophysics outreach, Strauss a renowned observational astronomer and Gott a theoretical cosmologist with other successful popular-science books to his name. The authors split the content of the book into three equal parts (stars and planets, galaxies, relativity and cosmology), making no attempt at stylistic uniformity. Apparently this was the intention, as they keep their distinct voices and refer frequently to their own research experiences to engage the reader. Despite this, the logical flow remains coherent, with a smooth progression in complexity.

*Welcome to the Universe* promises and delivers a lot. Non-scientist readers will get a rare opportunity to be taken from a basic understanding of the subject to highly advanced content, not only giving them the “wow factor” (although the authors do appeal to this a lot) but also approaching the same level of depth as a masters course in physics. A representative example is the lengthy derivation of E = mc^{2}, the popular formula that everyone is familiar with but few know how to explain. And while that particular example is probably demanding to the layperson, most chapters are very pleasant to read, with a good balance of narration and analysis. The authors also make a point of explaining why recognised geniuses such as Einstein and Hawking got their fame in the first place. Scientifically-educated readers will find many insights in this volume too.

While I generally praise this book, it does have a few weak points. Some of the explanations are non-rigorous and confusing at the same time (an example of this is the sentence: “the formula has a constant *h* that quantises energy”). In addition, an entire chapter boasts of the role of one of the authors in the debate on whether Pluto has the status of a planet or not, which I found a bit out of place. But these issues are more irritating than harmful, and overall this book achieves an excellent balance between clarity and accuracy. The authors introduce several original analogies and provide an excellent non-technical explanation of the counterintuitive behaviour of the outer parts of a dying star, which expand while the inner parts contract.

I also appreciated the general emphasis on how measurements are done in practice, including an interesting digression on how Cavendish measured Newton’s constant more than two centuries ago. However, there are places where one feels the absence of such an explanation, for example, the practical limitations of measuring the temperatures of distant bodies are glossed over with a somewhat patronising “all kinds of technical reasons”.

This text comes with a problem book that is a real treasure trove. The exercises proposed are very diverse, reflecting the variety of audiences that the authors clearly target with their book. Some are meant to practice basic competences about units, orders of magnitude and rounding. Others demand readers to think outside of the box (e.g. by playing with geodesics in flatland, we see how to construct an object that is larger inside than outside, and have to estimate its mass using only trigonometry). For some of the quantitative exercises, the solution is provided twice: once in a lengthy way and then in a clever way. People more versed in literature than mathematics will find an exercise that demands you write a scientifically accurate, short science-fiction story (guidelines for grading are offered to the teachers) and one that simply asks, “If you could travel in time, which epoch would you visit and why?”

The book ends with a long and inspiring digression on the role of humans in the universe, and Gott’s suggestion of using the Copernican principle to predict the longevity of civilisations – and of pretty much everything – is definitely food for thought.

*Andrea Giammanco, UCLouvain, Louvain-la-Neuve, Belgium*

### What goes up… Gravity and Scientific Method

*By Peter Kosso*

**Cambridge University Press**

Peter Kosso states that his book is “about the science of gravity and the scientific method”; I would say that it is about how scientific knowledge develops over time, using the historical evolution of our understanding of gravity as a guiding thread. The author has been a professor of philosophy and physics, with expert knowledge on how the scientific method works, and this book was born out of his classes. The topic is presented in a clear way, with certain subjects explored more than once as if to ensure that the student gets the point. The text was probably repeatedly revised to remove any wrinkles in its surface and provide smooth reading, setting out a few basic concepts along the way. The downside of this “textbook style” is that it is unexpectedly dry for a book aimed at a broad audience.

As the author explains, a scientific observation must refer to formal terms with universally-agreed meaning, ideally quantifiable in a precise and systematic way, to facilitate the testing of hypotheses. Thinking in the context of a certain theory will specify the important questions and guide the collection of data, while irrelevant factors are to be ignored (Newton’s famous apple could just as well have been an orange, for example). But theoretical guidance comes with the risk that the answers might too easily conform to the expectation and, indeed, the nontrivial give-and-take between theory and observation is a critical part of scientific practice. In particular, the author insists that it is naïve to think that a theory is abandoned or significantly revised as soon as an experimental observation disagrees with the corresponding prediction.

Considering that the scientific method is the central topic of this book, it is surprising to notice that no reference is made to Karl Popper and many other relevant thinkers; this absence is even more remarkable since, on the contrary, Thomas Kuhn is mentioned a few times. One might expect such a book to reflect a basic enlightenment principle more faithfully: the price of acquiring knowledge is that it will be distorted by the conditions of its acquisition, so that keeping a critical mind is a mandatory part of the learning process. For instance, when the reader is told that the advancement of science benefits from the authority of established science (the structural adhesive of Kuhn’s paradigm), it would have been appropriate to also mention the “genetic fallacy” committed when we infer the validity and credibility of an idea from our knowledge of its source. The author could then have pointed the interested reader to suitable literature, one option (among many) being *Kuhn vs. Popper; the struggle for the soul of science* by Steve Fuller.

*What goes up…* is certainly an excellent guide to the science of gravity and its historical evolution, from the standpoint of a 21st-century expert. It is interesting, for instance, to compare the “theories of principle” of Aristotle and Einstein with the “constructive theory” of Newton. While Newton started from a wealth of observations and looked for a universal description, unifying the falling apple with the orbiting Moon, Einstein gave more importance to the beauty of the concepts at the heart of relativity than to its empirical success. I enjoyed reading about the discovery of Neptune from the comparison between the precise observations of the orbit of Uranus and the Newtonian prediction, and about the corresponding (unsuccessful) search for the planet Vulcan, supposedly responsible for Mercury’s anomalous orbit until general relativity provided the correct explanation. And it is fascinating to read about the “direct observation” of dark matter in the context of the searches for Neptune and Vulcan. It is important (but surely not easy) to ensure “that a theory is accurate in the conditions for which it is being used to interpret the evidence”, and that it is “both well-tested and independent of any hypothesis for which the observations are used as evidence”.

The text is well written and accessible. My teenage children learned about non-Euclidean geometry from figures in the book and were intrigued by the thought that gravity is not a force field but rather a metric field, which determines the straightest possible lines (geodesics) between two points in space–time. I think, however, that progress in humankind’s understanding of gravity and related topics could be narrated in a more captivating way. People who prefer more vivid and passionate accounts of the lives and achievements of Copernicus, Brahe, Kepler, Galileo, Newton and many others would more likely enjoy *The Sleepwalkers* by Arthur Koestler or *From the Closed World to the Infinite Universe* by Alexandre Koyré. I also vehemently recommend chapter one of *Only the Longest Threads* by Tasneem Zehra Husain, a delightful account of Newton’s breakthrough from the perspective of someone living in the early 18th century.

*Carlos Lourenço, CERN*

**Books received**

### Gravitational Lensing

*By Scott Dodelson*

**Cambridge University Press**

Based on university lectures given by the author, this book provides an overview of gravitational lensing, which has emerged as a powerful tool in astronomy with numerous applications, ranging from the quest for extrasolar planets to the study of the cosmic mass distribution.

Gravitational lensing is a consequence of general relativity (GR): the gravitational field of a massive object causes light rays passing close to it to bend and refocus somewhere else. As a consequence, any treatment of this topic has to make reference to GR theory; nevertheless, as the author highlights, not much formalism is required to learn how to apply lensing to specific problems. Thus, using very little GR and not too complex mathematics, this text presents the basics of gravitational lensing, focusing on the equations needed to understand the phenomenon. It then dives into a number of applications, including multiple images, time delays, exoplanets, microlensing, cluster masses, galaxy shape measurements, cosmic shear and lensing of the cosmic microwave background.

Written with a pedagogical approach, this book is meant as a textbook for one-semester undergraduate or graduate courses. But it can also be used for independent study by researchers interested in entering this fascinating and fast-evolving field.

## Quantum Fields: From the Hubble to the Planck Scale

*By Michael Kachelriess*

**Oxford University Press**

This book treats two fields of physics that are usually taught separately – quantum field theory (QFT) on one side and cosmology and gravitation on the other – in a more unified manner. Kachelriess uses this unusual approach because he is convinced that, besides studying a subject in depth, what is often difficult is to put the pieces into a general picture. Thus, he makes an effort

to introduce QFT together with its most important applications to cosmology and astroparticle physics in a coherent framework.

The path-integral approach is employed from the start and the use of tools such as Green’s functions in quantum mechanics and in scalar field-theory is illustrated. Massless spin-1 and spin-2 fields are introduced on an equal footing, and gravity is presented as a gauge theory in analogy with the Yang–Mills case. The book also deals with various concepts relevant to modern research, such as helicity methods and effective theories, as well as applications to advanced research topics.

This volume can serve as a textbook for courses in QFT, astroparticle physics and cosmology, and students interested in working at the interface between these fields can certainly appreciate the uncommon approach used. It was also the intention of the author to make the book suitable for self study, so all explanations and derivations are given in detail. Nevertheless, a solid knowledge of calculus, classical and quantum mechanics, electrodynamics and special relativity is required.

### The Cosmological Singularity

*By Vladimir Belinski and Marc Henneaux*

**Cambridge University Press**

This monograph discusses at length the structure of the general solution of the Einstein equations with a cosmological singularity in Einstein-matter systems in four and higher space–time dimensions, starting from the fundamental work of Belinski (the book’s lead author), Khalatnikov and Lifshitz (BKL) – published in 1969.

The text is organised in two parts. The first, comprising chapters one to four, is dedicated to an exhaustive presentation of the BKL analysis. The authors begin deriving the oscillatory, chaotic behaviour of the general solution for pure Einstein gravity in four space–time dimensions by following the original approach of BKL. In chapters two and three, homogeneous cosmological models and the nature of the chaotic behaviour near the cosmological singularity are discussed. In these three chapters, the properties of the general solution of the Einstein equation are studied in the case of empty space in four space–time dimensions. The fourth chapter instead deals with different systems: perfect fluids in four space–time dimensions; gauge fields of the Yang–Mills and electromagnetic types and scalar fields, also in four space–time dimensions; and pure gravity in higher dimensions.

The second part of the book (chapters five to seven) is devoted to a model in which the chaotic oscillations discovered by BKL can be described in terms of a “cosmological billiard” system. In chapter five, the billiard description is provided for pure Einstein gravity in four dimensions, without any simplifying symmetry assumption, while the following chapter extends this analysis to arbitrary higher space–time dimensions and to general systems containing gravity coupled to matter fields. Finally, chapter seven covers the intriguing connection between the BKL asymptotic regime and Coxeter groups of reflections in hyperbolic space. Four appendices complete the treatment.

Quite technical and advanced, this book is meant for theoretical and mathematical physicists working on general relativity, supergravity and cosmology.