To Arianna, Carmen, Isabelle, and María José

When neutrinos first came on the scene in 1930, their father, Wolfgang Pauli, confessed to his colleague, the astronomer Walter Baade, that to save energy conservation in β-decays (quoted in Hoyle, 1967),

This was perhaps the only time Pauli was mistaken. Less than 30 years later, neutrinos were discovered by Reines and Cowan.

Since then, we have learned so many things about neutrinos that Pauli himself would be very surprised. More than this, understanding neutrino properties has always brought new insights into the whole field of fundamental interactions, and new theoretical paradigms.

Today we know quite accurately how to describe their feeble interactions with matter, from the very first attempts of Fermi to the succesful Standard Model of electroweak interactions. Many pieces of information have been collected in laboratory experiments, the traditional setting of particle physics. The study of neutrino interactions has been pursued at accelerators and reactors and, more recently, by sending neutrino beams produced at accelerators to underground laboratories. Accelerator experiments have also confirmed that there are only three generations of light neutrinos which are weakly interacting.

A Tale of Three Numbers:1, 3 and ∞. This might be a good subtitle for this chapter, which is about the problem of baryogenesis in the early universe.

We have already mentioned in Chapter 1 that observations of the light nuclear yields produced during primordial nucleosynthesis and the features of the CMB anisotropies single out a definite value for 1 parameter, the baryon-to-photon density ratio ηB ~ 6 × 10−10 at low temperatures, much below the nucleon mass. If the universe's expansion were starting with symmetric initial conditions, i.e., a zero initial baryon number per comoving volume, and no baryon-violating interactions were at work at all stages of this expansion, ηB would be expected to be much smaller, as we will show in the following. Moreover, we should detect a comparable number of antibaryons in the solar system or on larger scales, such as our galaxy (30 kpc) or the Local Group (3 Mpc). However, this is not what we do observe. Baryogenesis is a collection of several theoretical ideas on how the tiny value of ηB might be dynamically produced at some stage of the universe's history. The number of models which have been proposed is quite large, although maybe not really∞! Despite their different particular properties, they all share some common features, because they should all fullfill three basic conditions which were first put forward by Sakharov quite long ago (Sakharov, 1967).

Why me? Why now? These are the kind of questions that cosmological neutrinos could ask themselves about the strange coincidence of relevant facts at the MeV range of temperatures. The four known forces of Nature all play a role in this very interesting epoch. When the universe was from one-tenth of a second to a few minutes old, neutrinos experienced decoupling from electromagnetic plasma while flavour neutrino oscillations became effective, and they witnessed electron–positron annihilations and in the meantime were involved in the business of fixing the initial conditions for the primordial production of light nuclei. All these processes, which in principle could have occurred in the early universe well separated in time, depend upon the values of a bunch of unrelated parameters such as the Fermi constant, the neutrino mixing angles and squared mass differences, the electron mass and the binding energy of nuclei, in particular that of deuterium. The fact that all these events take place almost simultaneously means that they cannot be understood by a back-of-the-envelope calculation. Once more neutrinos put out a challenge to physicists.

In this chapter we first consider in Section 4.1 the process of relic neutrino decoupling in more detail than in Chapter 2, going beyond the instantaneous decoupling approximation in which neutrinos simply no longer interact with other particles below a certain temperature TνD. To this end, one should solve the Boltzmann integro-differential equations for the neutrino momentum distributions, with essentially no approximations.

The statistical properties of CMB temperature and polarization anisotropy maps encode very precise information on the history and composition of our universe. They depend primarily on the behaviour of inhomogeneities in the photon and baryon medium until photon decoupling, which feels all other species in two ways: through their impact on the cosmological background evolution, and via their contribution to the local gravitational forces. This is why neutrinos play an indirect yet important role in the physics of CMB anisotropies, and why present (and future) data on these observables give us quite remarkable pieces of information on neutrino properties.

To understand this point quantitatively, we need to follow photon decoupling at a much more detailed level than in Section 2.4.1. This is the subject of Section 5.1, where we overview the main features of CMB physics, of cosmological perturbation equations, the different contributions to the spectrum of CMB temperature anisotropies, and the effect of each cosmological parameter on the CMB spectrum. Neutrinos will appear on stage in Section 5.2, where we focus on the evolution of their perturbations until photon decoupling, and in Section 5.3, where we infer the effect of neutrino abundance, masses and properties on CMB anisotropies. Finally, Section 5.4 is a brief summary of recent constraints on neutrino properties, exploiting CMB data alone.

Cosmology is the quantitative study of the properties and evolution of the universe as a whole. Since the discovery of the redshift–distance relationship by Hubble in 1929, observations have supported the idea of an expanding universe, which can be beautifully described in terms of the Friedmann and Lemaître solution of the Einstein equations. The basis of this solution is the empirical observation that on sufficiently large scales, and at earlier times, the universe is remarkably homogeneous and isotropic. This experimental fact has been promoted to the role of a guiding assumption, the Cosmological Principle. Assuming that our observation point is not privileged, in the spirit of the Copernican revolution, one is naturally led to the conclusion that all observations made at different places in the universe should look pretty much the same independent of direction. Homogeneity and isotropy single out a unique form for the spacetime metric, the basic ingredient of Einstein theory. Cosmological models can then be quantitatively worked out after specification of the matter content, which acts as the source for curvature. Results can be then compared with astrophysical data, which in the last decades have reached a remarkable precision.

Actually, the Cosmological Principle works only on scales larger than 100 Mpc, yet it is a powerful assumption. In fact, several observables, such as the distribution in the sky of the cosmic microwave background (CMB), show inhomogeneities which are quite small, so that they can be treated as perturbations of a reference model (i.e., a reference metric) which is homogeneous and isotropic.

People used to think that the Solar System was essentially the entire Universe, and that beyond its bounds lay little more than “lots of stars.” We now know this is not so, and that the full astronomical Universe is far richer than that. Our Solar System is one among many, one small part of the whole. I like to think of it as our astronomical home base: the “house” in which we live.

We will begin to study our “house” by considering its most general features. We will ask how big it is and how massive; and what the orbits are of the bodies within it. The Solar System turns out to have a strikingly regular shape, and the planets within it divide naturally into two groups: inner and outer. In subsequent chapters we will focus more closely on its individual members.

Measuring the Solar System

In Part I of this book we prepared ourselves for our study of astronomy. In particular, we amassed a set of tools that we can use to measure various properties of the Universe. Let us now use these tools to find:

(1) the size of the Solar System,

(2) the sizes of the Sun and planets,

(3) the masses of the Sun and planets.

(1) The size of the Solar System

To measure the size of the Solar System we need to measure the sizes of orbits within it. We will begin by measuring the size of our orbit, and then move on to that of the planets.

Astronomy belongs to everyone. The Universe is here for all of us to see. Its study is not just the province of astronomers, with their expensive telescopes and strange, unfamiliar mathematics. In this chapter, we are concerned with astronomy that you can do with your naked eye.

Some of the most universal aspects of our lives are influenced by astronomical phenomena. Imagine, for instance, a world in which day did not turn into night, or one in which there were no seasons! As we think about these, we will quickly realize that they are more subtle than perhaps we had thought. Indeed, even so simple a thing as the daily path of the Sun across the sky was historically explained in several different ways.

So too with eclipses and the phases of the Moon, the measurement of time and the drifting of the Sun along the zodiac – we begin our voyage through the Universe with these, some of the most fundamental aspects of our everyday environment.

Rising and setting: the rotation of the Earth

Perhaps the most basic of all astronomical observations is the simple fact that day turns into night and then day again in a never-ending cycle. This perpetual alteration, caused by the passage of the Sun across the sky, is so familiar that we hardly ever stop to pay attention to it. But in fact there is more to it than many people think.

Let us begin our study of astronomy with this, perhaps the simplest of all astronomical observations: the study of the Sun’s path across the sky. To perform this study you will need no advanced scientific equipment. Simply step outside just before dawn, face east, and watch what happens. What you see depends on where you live: we will concentrate on the view of the sky from the mid northern hemisphere.

Introducing galaxies and the Universe

So far we have surveyed what might be called our corner of the cosmos: a region of space extending outward several thousand light years. We now extend our vision much farther – to the very edge of the known Universe. In doing so we will find a new and previously unsuspected structure: galaxies. Everything we have so far studied – the Earth, the Sun and all the Solar System; the stars visible to the naked eye and the more distant stars that telescopes reveal; interstellar clouds – all these are part of an enormous structure known as the Milky Way Galaxy. Lying beyond our Galaxy lie other galaxies, billions and billions of them, stretching out to the farthest bounds of the Universe.

It is difficult to comprehend the immensity of the distances we are about to encounter. A ray of light, which can cross the Atlantic Ocean in 0.02 seconds, would require a hundred thousand years to cross our Galaxy. Even the nearby galaxies lie millions of light years from us. Light from a distant galaxy began its journey toward us long before the Earth was formed.

As we saw in Chapter 8, finding new planets is hard. Uranus, the first planet not visible to the naked eye, was discovered in 1781, Neptune in 1846 and Pluto in 1930. That works out to only one new planet in each of the last three centuries! But in recent years the pace of discovery has accelerated spectacularly. A new planet was discovered in 1995; by now more than a thousand potential candidates have been found. Plans are under way for yet more dramatic advances in technology, which should greatly improve our ability to find these new worlds.

Most remarkable of all is that none of these new planets orbits our own Sun. They are orbiting the distant stars.

These discoveries have completely changed our view of our place in the Universe. Until the first of these new worlds was discovered, for all we knew our own Solar System might have been unique. If so, we would have been utterly alone in the cosmos. But by now we know that planets are common. This has dramatic implications for the search for life elsewhere in the Universe.

Direct detection of extrasolar planets

How have these far-distant worlds been found? You might think that they were discovered in just the same way that planets in our own Solar System were: just by looking for them through a telescope. Remarkably, however, this was not the case. In almost every case, even though we know of their existence, we have never seen these new worlds.

We closed Chapter 12 on the “census of stars” with a question: what is the significance of the three categories of stars: main sequence, red giant and white dwarf? In Chapter 14 we reached an understanding of main sequence stars: they are powered by thermonuclear reactions that transform hydrogen into helium. In this chapter we move on to red giants and white dwarfs.

We can think of the hydrogen in a main sequence star as fuel that powers its shining. In the previous chapter we explained that a star has lots of hydrogen, so that it can continue shining for a long time. But no matter how long this can go on, eventually the star will run out of this fuel. You might think that, once this happens, the star will simply go out. But it turns out that helium, the residue of hydrogen reactions, is itself a fuel. In order to use this new fuel, the star must readjust its structure to become a red giant. Indeed, the subsequent evolution of a star is governed by a whole series of other such readjustments.

But this process cannot go on forever. Eventually, no more fuel will be left to the star. Again, you might think that, once this happens, the star will simply “die.” But it does not die. Instead, the star is utterly reborn as a new and exciting “corpse” – a white dwarf, a neutron star, a black hole or a cataclysmic supernova.

Are we alone, or does life exist elsewhere in the Universe? We have never found convincing evidence of life on other worlds. But there are reasons to think that extraterrestrial life is possible. On the one hand, the Earth does not appear to be unique in any way: what happened here can very well also happen somewhere else. And on the other hand, there are an awful lot of these “somewhere elses” in the Universe: there are many stars in our Galaxy, and many galaxies in the cosmos.

In our discussion we will deal solely with life as we know it, similar to the form we find on Earth: life that evolves by mutation and natural selection, life based on carbon chemistry and employing DNA as the carrier of genetic information. Other kinds are at least conceivable. There have been speculations about a form of life based on silicon. Science fiction writers have imagined far stranger possibilities. But we will not consider these, for the simple reason that we don't know anything about them. The only life about which we know anything at all is the kind that exists on Earth: concerning other varieties, we can only speculate.

Searches have been conducted for life on Mars, and searches are under way right now for signals from extraterrestrial civilizations. These searches have found nothing persuasive so far, and nobody thinks their task will be easy. But it is no exaggeration to say that the discovery of life elsewhere in the Universe would be one of the greatest scientific triumphs of all time.