The detection of fluctuations in the sky temperature of the cosmic microwave background (CMB) by the COBE team (Smoot et al. 1992) was an important milestone in the development of cosmology. Aside from the discovery of the CMB itself, it was probably the most important event in this field since Hubble's discovery of the expansion of the universe in the 1920s (Hubble 1929). The importance of the COBE detection lies in the way these fluctuations are supposed to have been generated, and their relation to the present matter distribution. As we shall explain shortly, the variations in temperature are thought to be associated with density perturbations existing at the epoch trec, when matter and radiation decoupled. If this is the correct interpretation, then we can actually look back directly at the power spectrum of density fluctuations at early times, before it was modified by non-linear evolution and without having to worry about the possible bias of galaxy power spectra.

The search for anisotropies in the CMB has been going on for around 25 years. As the experiments got better and better, and the upper limits placed on the possible anisotropy got lower and lower, theorists concentrated upon constructing models which predicted the smallest possible temperature fluctuations. The baryononly models of the 1970s were discarded primarily because they could not be modified to produce low enough CMB fluctuations. The introduction of dark matter allowed such a reduction and the culmination of this process was the introduction of bias, which reduces the expected temperature fluctuation still further.

One of the great successes of the hot-big-bang model is the agreement between the observed abundances of light elements and the predictions of nucleosynthesis calculations in the primordial fireball. However, this agreement can only be made quantitative for certain values of physical parameters, particularly the number of light neutrino types, neutron half-life and cosmological entropyper-baryon. Since the temperature of the cosmic microwave background radiation is now so strongly constrained, the latter dependence translates fairly directly into a dependence of the relative abundances of light nuclei upon the contribution of baryonic material to Ω0. It is this constraint, the way it arises and its implications that we shall discuss in this chapter. For more extensive discussions of both theoretical and observational aspects of this subject, see the technical review articles of Boesgaard & Steigman (1985), Bernstein et al. (1988), Walker et al. (1991) and Smith et al. (1993).

Theory of nucleosynthesis

Prelude

We begin a brief description of the standard theory of cosmological nucleosynthesis in the framework of the big-bang model with some definitions and orders of magnitude. The abundance by mass of a certain type of nucleus is the ratio of the mass contained in such nuclei to the total mass of baryonic matter contained in a suitably large volume. As we shall explain, the abundance of 4He, usually indicated with the symbol Y, has a value Y ≃ 0.25, or about 6% of all nuclei, as determined by various observations (of diverse phenomena such as stellar spectra, cosmic rays, globular clusters and solar prominences).

This book had its origins in a coffee-time discussion in the QMW common room in 1993, in the course of which we discussed many issues pertaining to the material contained here. At the time we had this discussion, there was a prevailing view, particularly among cosmologists working on inflationary models, that the issue of the density of matter in the Universe was more-or-less settled in favour of a result very near the critical density required for closure. Neither of us found the arguments made in this direction to be especially convincing, so we determined at that time to compile a dossier of the arguments – theoretical and observational, for and against – in order to come to a more balanced view. This resulted in a somewhat polemical preprint, ‘The Case for an Open Universe’, which contained many of the arguments we now present at greater length in this book, and which was published in a much abridged form as a review article in Nature (Coles & Ellis 1994).

The format of a review article did not, however, permit us to expand on the technical aspects of some of the arguments, nor did it permit us to foray into the philosophical and methodological issues that inevitably arise when one addresses questions such as the origin and ultimate fate of the Universe, and which form an important foundation for the conclusions attained. The need for such a treatment of this question was our primary motivation for writing this book.

In this chapter we shall discuss the dark matter inferred from astrophysical measurements. We divide these astrophysical arguments into three broad categories: galaxies, rich clusters of galaxies and the intergalactic medium. Because astrophysical processes (with the exception of gravitational effects) generally involve baryonic material only, the constraints we discuss frequently, though not exclusively, relate only to the baryonic contribution to the total density. We shall discuss constraints from large-scale structure in the matter distribution (i.e. clustering on scales greater than the scale of individual rich clusters) in the next chapter. For an extensive and influential survey of much of the astrophysical evidence see Peebles (1971), which serves as a standard reference for much that we discuss in this chapter; see also Faber & Gallagher (1979).

Galaxies

It was suggested as early as the 1930s that the total amount of matter in our own galaxy, the Milky Way, is greater than can be accounted for by the visible matter within it (e.g. Oort 1932). We shall not, however, go into any detail here concerning the evidence from stellar dynamics that there is dark matter in the disk of the Milky Way; see, for example, Bahcall (1984). This is still an open question. What we are interested in is the evidence for massive haloes of dark matter surrounding our own and other galaxies.

The mass-to-light ratio

Before discussing the evidence for dark matter in galaxies and clusters, we need to introduce some notation.

The issue

The issue we plan to address in this book, that of the average density of matter in the universe, has been a central question in cosmology since the development of the first mathematical cosmological models. As cosmology has developed into a quantitative science, the importance of this issue has not dimininished and it is still one of the central questions in modern cosmology.

Why is this so? As our discussion unfolds, the reason for this importance should become clear, but we can outline three essential reasons right at the beginning. First, the density of matter in the universe determines the geometry of space, through Einstein's equations of general relativity. More specifically, it determines the curvature of the spatial sections: flat, elliptic or hyperbolic. The geometrical properties of space sections are a fundamental aspect of the structure of the universe, but also have profound implications for the space-time curvature and hence for the interpretation of observations of distant astronomical objects. Second, the amount of matter in the universe determines the rate at which the expansion of the universe is decelerated by the gravitational attraction of its contents, and thus its future state: whether it will expand forever or collapse into a future hot big crunch. Both the present rate of expansion and the effect of deceleration also need to be taken into account when estimating the age of the universe.

As we mentioned in Chapter 1, the main reasons for a predisposition towards a critical density universe are theoretical. We will address these issues carefully, but please be aware at the outset of our view that, ultimately, the question of Ω0 is an observational question and our theoretical prejudices must bow to empirical evidence.

Simplicity

In the period from the 1930s to the 1970s, there was a tendency to prefer the Einstein–de Sitter (critical density) model simply because – consequent on its vanishing spatial curvature – it is the simplest expanding universe model, with the simplest theoretical relationships applying in it. It is thus the easiest to use in studying the nature of cosmological evolution. It is known that, on the cosmological scale, spatial curvature is hard to detect (indeed we do not even know its sign), so the real value must be relatively close to zero. Moreover, many important properties of the universe are, to a good approximation, independent of the value of Ω. The pragmatic astrophysicist thus uses the simplest (critical density) model as the basis of his or her calculations – the results are good enough for many purposes (e.g. Rees 1995).

There are, in addition to this argument from simplicity, a number of deeper theoretical issues concerning the Friedman models which have led many cosmologists to adopt a stronger theoretical prejudice towards the Einstein–de Sitter cosmology than is motivated by pragmatism alone.

We now turn our attention to the evidence from observations of galaxy clustering and peculiar motions on very large scales. In recent years this field has generated a large number of estimates of Ω0 many of which are consistent with unity. Since these studies probe larger scales than the dynamical measurements discussed in Chapter 5, one might be tempted to take the large-scale structure as providing truer indications of the cosmological density of matter. On the other hand, it is at large scales that accurate data are hardest to obtain. Moreover, very large scale structures are not fully evolved dynamically, so one cannot safely employ equilibrium arguments in this case. The result is that one is generally forced to employ simplified dynamical arguments (based on perturbation theory), introduce various modelling assumptions into the analysis, and in many cases adopt a statistical approach. The global value of Ω0 is just one of several parameters upon which the development of galaxy clustering depends, so results are likely to be less direct than obtained by other approaches. Moreover, it may turn out that the gravitational instability paradigm, which forms the basis of the discussion in this chapter, is not the right way to talk about structure formation. Perhaps some additional factor, such as a primordial magnetic field (Coles 1992) plays the dominant role. Nevertheless, there is a persuasive simplicity about the standard picture and it seems to accommodate many diverse aspects of clustering evolution, so we shall accept it for the sake of this argument.

Excerpts of the letter referred to in this note appear in Appendix C.

Dear Colleagues,

Though the attached letter to prospective participants of your Colloquium provides most of the essential information, let me emphasize that the success of the Colloquium will depend on the skills of the moderators.

The attached letter will be mailed to all prospective panelists together with the invitation. We hope that its message is clear, and that it will make your chore easier.

As soon as the final composition of your panel of discussants is clear, we will ask you to contact them and to obtain a rough outline of the issues they wish to present. Thereafter, it will be up to you to coordinate the sequence of presentations, and to familiarize all panelists with the issues to be considered.

Hopefully, you will be able to prevent talks that exceed 10 minutes. If the discussants adhere to the time schedule, there will be 40–50 minutes for a general discussion with questions from the audience.

Most scientific meetings involve more than one type of event. One can look at these events as building blocks, and it is their combination and placement that will be instrumental for the success of the meeting (see Chapter 5). The following listing is arbitrary and merely highlights options that can be modified to suit a particular situation.

Scientific events

Lectures

All good lectures have one thing in common: they are not too long. It seems that all over the world the attention span has shrunk during recent decades. Blame it on our hectic lifestyle or the impact of the mass media: most people get restless when lectures exceed one hour.

To prevent monotony, lectures (with the possible exception of Main Lectures) should be followed by a discussion period and a break. The length of the break must vary with the circumstances, as detailed in the following sections. However, even ‘Short Communications’ should be scheduled at least three minutes apart. During sessions with several consecutive lectures, one or two extended breaks are definitely indicated (see below).

Within a series of lectures, it is imperative to leave the time slot unused if a speaker does not show up, unless the change can be announced well in advance. Otherwise, participants may miss the event. Any change of schedule during a meeting is likely to cause confusion.

Punctuality of lectures is a must when parallel sessions are held. A cautionary example: At an international conference convened in a country known for its ‘relaxed’ lifestyle, the projectionists appeared routinely late after lunch and resumed their jobs at different times.

The best times for scientific meetings are probably the pre- and post-seasons. The advantages are obvious: reasonably good weather, no mass tourism, reduced room rates, and frequently lower airfares. In most of Europe, weather conditions make late spring and early autumn equally attractive; in the southeastern United States and the Caribbean region, on the other hand, the hurricane season (from about August to December) is a risk factor for larger meetings. Similar considerations apply to many places in southern and eastern Asia with seasonal typhoons. Also, it will not create fond memories when your participants grow mildew on their heads while waiting for the repair of a bridge during the monsoon. Of course, it also does not make sense to select locations where snow or ice could prevent participants from either arriving or leaving. Will you pay for their rooms when they are trapped for days in an expensive airport hotel? Furthermore, don't choose a time when many families traditionally get together, i.e., in particular between Christmas and New Year. Last but not least, remember that air fares may be extremely high at the weekend. This could be a deterrent for prospective participants when a meeting closes on a Friday or Saturday.

There is one more factor to consider: special local events. No matter what type of meeting you envision, make sure that your meeting does not clash with an event that causes local overcrowding of roads, parking lots, restaurants, hotels, etc. Typical examples would be major conventions or sports events.

There is one overriding principle for the selection of your office staff: a few thinking people. Do not fall to the temptations of status display and hire people you don't need; and don't try to save money by hiring cheap labor. You will be better off paying good people overtime than employing helpers who need all the help they can get.

The ideal person for the office of a smaller meeting would be a secretary who has organizational talents, writes flawless English, is familiar with scientific terminology, is a good proof-reader, is experienced in the use of computers; and, above all, is reliable. Unfortunately, they don't always make them that way.

For a larger meeting, you may split the work between an assistant and a person mainly involved in typing. The job of the assistant includes the mailing of announcements and various types of forms, book- and budget-keeping, monitoring the timely submission of payments and scientific material (e.g., abstracts, questionnaires), and answering routine letters and e-mail. Ultimately, the assistant will also be in charge of the registration desk, even if it is staffed by employees of a professional service, or of a society (see below). The typist will handle most of the typing, from letters to forms, abstracts, manuscripts, etc. Familiarity with word processing is essential, particularly since the typist will have to update and correct continuously a list of addresses that can be transferred to mailing labels. The respective roles of the assistant and typist must be clearly understood from the beginning, and one of them must be replaced instantly if they cannot cooperate.

Some food for thought

I have been touched by the decency of colleagues who were not well off financially and yet asked to give their share of travel support to younger researchers. On the other hand, I have been appalled by the avarice and egotism of some very illustrious and well-to-do scientists.

The first time I had to allocate funds for a meeting, I called up the invited speakers as soon as I had received the award. Joyfully, I asked the first fellow if several hundred dollars would be helpful for his travel arrangements. The answer was prompt: ‘No, not really.’ Dazzled, I asked if that meant he would not come. In a diplomatic reflex, he then assured me that he was very happy to accept the money.

Some scientists seem to believe that the rules of a bazaar also apply to requests for travel support. They ask for outrageous amounts hoping that this will garner them the lower amount they are actually shooting for. Some of my friends have become so allergic to this attitude that they look with apprehension at any scientist from certain nations.

Similarly unpleasant is the expectation of some retired scientists to receive lavish travel support for meetings they have attended for decades. Of course, you want them to come, but how can you justify paying for suites for them if you don't have enough funds to pay for beds for outstanding younger colleagues? What granting agency would approve an application requesting preferential funding for retired honorees?

General audience

Sometimes, an organizer must decide if a meeting should be open to all those interested, or restricted to a certain audience. Since restrictions often create animosity, it is better to avoid them if possible.

Meetings with restricted audiences, such as the Gordon Conferences, may be desirable for confidentiality and/or in-depth discussions. To keep bad feelings to a minimum, however, one should be honest about the purpose of ‘closed’ meetings, and the rules that apply. Blackball schemes have a tendency to backfire, sometimes to the point of ostracism of the organizer. As they say, every dog will have his day.

Of course, the difference between ‘open’ and ‘closed’ meetings can be blurred. For instance, when a society raises the convention fee for non-members to prohibitively high levels; or, when someone convenes a conference in a place with limited overnight accommodation, and fills the available rooms with friends.

The weirdest proposal I ever came across requested funds for a special conference. The audience was limited to the number of seats in a small room. And how were the participants to be selected? By inviting everybody interested to submit an application that was to be reviewed by the organizer – who himself had no research funds whatsoever!

Question: Why should anyone pretend a de facto closed meeting is ‘open?’

Answer: In general, public money is easier to get for ‘open’ meetings.

In some fields of research, growing numbers of participants have changed the family atmosphere of the conferences.