We now move on to discuss the second face of the problem of the cosmological constant, which was highlighted recently by the discovery of the acceleration of the universe. This chapter will first review briefly how searching for “dark energy” has come finally to a spatially flat universe well described by a cosmological constant Λ of a size smaller than but nearly comparable to the critical density. For a number of reasons, we consider that this Λ is not a true constant but is mimicked most naturally by a scalar field.

In section 5.1, we sketch what the development has been like mainly on the observational front, culminating in the conclusion that we have an accelerating universe.

As a possible theoretical model discussed recently, we first review in section 5.2 the results of “quintessence,” a name mainly indicating a cosmological scalar field. Since this is a phenomenological approach that is not necessarily constrained rigorously by the scalar–tensor theory, our focus is mainly on the assumed inverse-power potential. A primary concern is the question of how naturally the initial conditions for the scalar field can be chosen. A relevant question is that of whether the scalar-field energy falls off in the same way as the ordinary matter density (“scaling”), or approaches the latter starting from different values (“tracking”).

As was emphasized in the preceding chapter, the way the scalar field enters the arena of the scalar–tensor theory is not simple. It does so through what is known as a nonminimal coupling term. This is a unique feature shared by those models qualified to be called scalar–tensor theories in the sense conceived by Jordan. In spite of the simplicity of wanting to implement a variable gravitational “constant,” this term is a somewhat contrived technical device that tends to obscure other issues of physical significance. One of the emphases in this chapter is placed on revealing them beyond mathematical manipulations.

Among several versions, or models, of the scalar–tensor theory, the one due to Brans and Dicke might be viewed as a “prototype.” This model, which is based on certain assumptions made for the sake of simplicity, is in fact over-simplified from the point of view of theoretical models of the modern unification program. Also for some other reasons, this model may not be accepted as fully realistic. Nevertheless, a prototype has its own merit that deserves careful and comprehensive understanding. In this chapter we introduce the original BD model as a basis of the subsequent developments.

Section 1 is an elementary but technical introduction to the prototype BD model as a basis of the whole discussion that follows.

The energy scale of processes that occur naturally on the surface of the Earth is relatively low. At these energies, the forces of nature are different from one another because the particles that transmit them have very different properties. However, above 1015 degrees the electromagnetic and weak forces become indistinguishable. That is, they take on similar identities. Indeed, such modifications have been observed in the large particle accelerators. This fundamental similarity between the electromagnetic and weak forces suggests that they might be two components of a more fundamental force. The two forces are said to become unified into the electroweak force above 1015 degrees.

What causes such a unification at this particular temperature? We know that temperature is just a measure of the amount of energy present; higher temperatures correspond to higher energies. Furthermore, energy and mass are equivalent. In this sense, then, mass is closely related to temperature. For every mass there is a corresponding energy and temperature.

The masses of the W and Z particles correspond to this temperature of 1015 degrees. These particles have two types of energy associated with them: one is the energy stored in their mass, and the other is the energy determined by how fast they are moving. This latter type is called kinetic energy. As the temperature increases, so does the kinetic energy of the particles. The energy stored in the mass remains fixed, however, because the masses of the particles are constant.

We are now in a position to talk meaningfully about the earliest stages of our universe's history. Over the last few decades a scenario has emerged that indicates that the universe began life as a rapidly expanding and intensely hot fireball. This picture is referred to as the big bang model. Most cosmologists agree that this model represents an accurate description of the very early universe, at least for times after about one second.

In this chapter we will trace the history of the universe from the big bang through to the present day. Let us begin by discussing some of the key principles that governed the behaviour of the universe during the big bang.

The temperature of the universe at any given time is directly related to the size and age of the universe. It often proves convenient to measure the age of the universe directly in terms of its temperature. A higher temperature then corresponds to an earlier time. For example, when the universe was one second old its temperature was about ten billion degrees. It will be useful to keep this temperature in mind for comparative purposes in our forthcoming discussion.

The very early universe was considerably hotter than ten billion degrees. Matter in the form of atoms would not have been present. Indeed, atoms did not come into existence until the universe was about three hundred thousand years old. Moreover, nuclei did not become stable until a few minutes had elapsed.

In Chapter 2, we discussed the very reliable observations that show that the universe is expanding at the present era. The current expansion of the universe represents the first argument in favour of the big bang model, although it is not proof by itself, as explained in Figure 4.3. Two other important observations support the model. The first is the relative abundances of hydrogen and helium in the universe. The second is the existence of cosmic radiation at the present era.

The amount of helium that was produced during the nucleosynthesis era of the big bang was determined by the relative numbers of neutrons and protons that were present at that time. These particles were formed shortly after the quark era, when the quarks became confined by the strong force. The universe was about 10−4 seconds old when this occurred. It took another three minutes or so for the universe to cool sufficiently for the synthesis of helium to be completed.

Thus, the neutrons and protons had to wait before they could begin to produce atomic nuclei. Because the mass of the neutron is slightly higher than that of the proton, the neutron has slightly more energy, and a free neutron may decay into a proton. What happens is that a down quark changes into an up quark, and this transformation is made possible by the weak interaction.

We live in a big universe. Even if we were able to travel across the universe at the speed of light, the journey would take us at least ten billion years. Why is the universe so large? Has the universe always been this big, or was it smaller in the past? If smaller, how small was it? Was there a time when the volume of the universe vanished?

We can ask related questions regarding matter in the universe. Why is the universe not empty? From where do the atoms that make up our bodies originate? When were these atoms created?

Questions such as these lead us inevitably to the origin of the universe. Did the universe have a definite beginning, or has it always existed? If it had a beginning, can we talk meaningfully about what might have happened beforehand? And what caused the universe to come into existence in the first place?

The purpose of this book is to address questions such as these. Moreover, because our own origin is linked with that of the universe as a whole, we are indirectly studying our own past when we investigate the beginning of the universe.

We will see that the structure of the universe is intimately related to the structure of the smallest elementary particles. This relationship between the world of the very large and that of the very small was manifest even during the first second of the universe's history.

In this chapter we will consider in what way the big bang model needs to be modified. Recall from the previous chapter that there are a number of shortcomings with the model, in particular, with the uniformity of the cosmic radiation. Let us reconsider this cosmic radiation further. Its uniform temperature is problematic because the model predicts that the horizon distance grows faster than the separation between two points in space.

Our assumption that the horizon distance grows more rapidly than the expansion of space may not always be correct in the environment of the very early universe. It is quite possible that space itself might have expanded faster than the horizon for a brief interval some time before the decoupling of radiation and matter took place. Suppose, for the moment that this had indeed been the case. How would it affect our conclusions regarding the cosmic radiation?

We could begin with a region of the universe that was much smaller than the horizon. Physical processes could have operated within this region to establish thermal equilibrium, and any temperature differences that might have existed could in principle be eliminated. If this region then grew at a faster rate than did the horizon, it would eventually come to exceed it.

The final result would correspond to Figure 8.3a when we identify the boundary of the initial region with the lines A and B.

Visible light is an example of electromagnetic radiation. This radiation may be pictured as a wave travelling through space. Although light always travels at a fixed speed, its wavelength – defined as the distance between two successive peaks or troughs – is not uniquely specified. Different types of light can have different wavelengths. These differences manifest themselves as different colours in the visible spectrum. For example, red light has a slightly longer wavelength than blue light. The light that we receive from the sun is a mixture of all the different colours.

Electromagnetic radiation with wavelengths significantly longer or shorter than those associated with visible light also exists. Two examples are gamma rays and radio waves. All types of electromagnetic radiation carry a certain amount of energy. A gamma ray has a lot of energy whereas a radio wave carries a relatively small amount of energy. In a sense, we can imagine the energy as localized around the peaks and troughs of the wave. Thus the energy of a given type of electromagnetic radiation is specified by its wavelength; a shorter wavelength corresponds to a higher energy and vice versa. This follows since a shorter wavelength means that more crests and troughs will arrive in a given interval of time, so more energy will be received.

Light has a very important property in that it changes its direction of motion as it travels between regions of different density.

If the stars in distant galaxies have the same composition as those in our own galaxy, the light we receive from them should exhibit the characteristic signatures of hydrogen and helium. This is indeed observed. However, there is one crucial difference between galactic and stellar light, and this has profound consequences for our understanding of the universe. Although it is true that the relative separation of the dark lines observed in the galactic light corresponds to hydrogen and helium atoms, the lines do not appear quite in their expected positions. When we examine the light from galaxies, we find that the dark lines have all been shifted slightly along the photograph.

Figure 3.1 shows schematic pictures of the light emitted by a typical star in our galaxy and the light received from an average distant galaxy. Light of a longer wavelength is positioned towards the right of the diagram. If this were a colour photograph, the picture would appear redder on the right-hand side and bluer on the left. Notice how the absorption lines in the galactic light are all positioned at slightly longer wavelengths than in the stellar case.

The key to understanding what causes the dark lines to be moved towards longer wavelengths lies in the fact that light travels through space as a wave. Consider what happens when a wave is emitted by a source and is then picked up by a receiver positioned some distance away.