NOTES ON COSMOLOGY The subject of cosmology is fundamentally different in nature from any other scientific subject, since by definition it deals with the entire Universe. There is only one Universe, so we can't compare it to others as we do when studying any of its components. And we can't get outside of it. We can't even define an edge, or a center. Theoretical descriptions of the Universe were put on a new mathe- matical footing with Einstein's publication of his General Theory of Relativity in 1918. Shortly thereafter, cosmology became an observational science with Hubble's discovery that the spectra of distant galaxies show redshifts that are proportional to their estimated distances. Interpre- ting the redshifts as velocities of recession, this gives us the velocity- distance relation (also known as the "Hubble Law"), which is considered to be due to a uniform expansion of the Universe. As far as we know, this relation holds at all distances. In recent years, with the construction of giant telescopes and a vastly improved ability to record the spectra of extremely faint light sources, cosmology has blossomed into one of the major branches of astronomy. In addition to this observational work, high-speed computers are used to model the Universe and, by numerical simulation, to follow its development. In this course we have time only to touch upon the main ideas of cosmology. Students wishing to pursue the subject in greater depth will find much more material in the textbook, and may wish to consider taking Professor David Weinberg's course, Astronomy 163, a follow-on course which devotes a whole quarter to cosmology. Astronomy 163 is usually offered in alternate years and will be given next in Autumn 2002. The following notes touch briefly upon topics that will be discussed in class, and which you should expect to be asked about on the Final Exam. In our textbook ("Universe"), read the first four sections of chapter 28 (pp. 640-649*); it is not necessary to study chapter 29. *[ 5th edition: pp. 698-707 ] Olbers' Paradox: What is the paradox, and how can it be resolved? The Cosmological Principle: What assumption do we make, and why do we make it? Implications of the Hubble Law (i.e. the velocity-distance relation). Try to imagine a uniformly expanding, infinite Universe -- one that has no center but does have a definite beginning in time. Note that if the amount of matter in the Universe stays the same, it must be "thinning out" due to the expansion, and interactions between particles are becoming less frequent. That is, the Universe is becoming less dense and colder. If these trends continue forever, the fate of the Universe is to become steadily colder, darker, emptier... Conversely, thinking backwards in time, the Universe of the past must have been hotter, brighter, and denser. Knowing (from the observed rate of recession of galaxies) the Universe's rate of expansion, we can calculate what the temperature, density, etc. were at any time in the past. But we know from laboratory experiments how atoms behave, and how atoms and photons interact, at different temperatures and densities, and so we can describe the conditions that prevailed long ago. If we work back far enough, we reach the extreme conditions (very energetic colli- sions between particles) that are produced in the world's largest atomic accelerators. Thus the study of the fundamental particles of nature ("particle physics") is closely allied to the study of cosmology. The same people study both the largest and the smallest things that we can imagine. So far we have been describing a model for the Universe popularly known as the Big Bang Theory -- an evolving (i.e. changing) Universe. Since we can, in principle, calculate how long ago the matter of the Universe was very hot and densely packed, such a Universe has a definite age. All changes proceed irrevokably in one direction: the density of matter in the Universe steadily drops as space expands, until a point is reached when conditions are favorable for galaxies to form, and for stars to form within galaxies; nuclear reactions in stellar interiors then change light elements into heavier ones, the heavy elements get locked up in white dwarfs, neutron stars, and black holes, and everything keeps getting colder and darker. Before considering some further implications of this model, let's address a question that one is bound to ask: Is there an alternative? Many people don't like the idea that the Universe has a definite age, or the conclusion that it will have such an undramatic end. Is there a way to imagine a Universe that is infinitely old, that will survive forever, and that will always have the same general characteristics that we observe today? This is indeed possible, and was the objective of the Steady State theory developed in England during the 1950s by Fred Hoyle and others. The basic idea of the Steady State theory is a generalization of the Cosmological Principle. While the usual Cosmological Principle states that the Universe looks the same no matter where you are, the Steady State cosmologists assumed further that the Universe has ALWAYS looked the same, i.e. it is not evolving. If that is true, there is no beginning or end. But we observe that galaxies are receding from one another, i.e. the Universe is expanding. How can it expand without the density dropping, and if the density changes, doesn't this contradict the starting assumption? The proponents of the Steady State theory answered by postulating the "continuous creation" of matter, in the form of simple protons and electrons, throughout space and at a rate that exactly compensates for the expension, keeping the density constant. If this seems too great a coincidence to be credible, it can be proposed that the expansion of the Universe may actually be caused by this creation of matter. One big problem with this theory is that the new matter has to be created out of nothing -- not merely by converting energy to matter -- and hence it violates the known conservation laws. But for some, having little miracles going on all over the Universe at all times is no harder to accept than having one gigantic miracle at the beginning. One nice thing about having two well-developed, opposing theories is that predictions can be made from them both, which can be compared to observation. Basically, any observation that shows that the Universe is changing with time would argue against the Steady State theory and hence in favor of the Big Bang theory. There are in fact several lines of evidence that the Universe of the distant past was quite unlike the present-day Universe. We can study the Universe of the distant past observationally simply by observing things that are extremely far away, so that their light has taken most of the age of the Universe to reach us. You should try to understand the following arguments; I will just sketch them briefly here but will try to explain them more fully in class. 1) All galaxies appear to have approximately the same age; we have not found any galaxies that seem to be, say, ten times older than our own. It appears that the Universe went through an epoch of galaxy formation. 2) Quasars -- on the assumption that their redshifts are due to the expansion of the Universe -- are not uniformly distributed through- out the Universe. There are none close to us, and thousands very far away, in all directions, i.e. in places that we see as they were a long time ago. It appears that quasars formed early in the history of the Universe and have subsequently died out. 3) The 3-degree background radiation, which peaks in the microwave region of the radio spectrum. You should review its observed properties, and understand how it can be accounted for in terms of the Big Bang theory. It is considered to consist of photons that were emitted when the Universe was young and hot, but at places so far away that this radiation is only now reaching us, highly redshifted. This "cosmic background radiation" has a natural explanation in the Big Bang theory (in fact it was predicted), but it is not accounted for by the Steady State theory. All these observational tests indicate that the Universe is an evolving one, contrary to the Steady State theory. The main reason for discussing the Steady State theory today is that it is instructive to consider the observational tests that disprove it, for that is why we are confident that the Universe is indeed evolving. In the 1950s, one of the primary motivations for studying cosmology was to see if the conditions in the Universe in the past were ever right for creating the array of chemical elements that we have today. These atomic nuclei must have been made somewhere -- were they created in the early Universe? By following the changes of temperature and density in the Big Bang model, it was found that conditions were, for a while, right for hydrogen fusion to take place via the proton-proton cycle, which converts hydrogen into helium, just as in stars. However, by the time about 25% of the matter had been turned into helium, the expansion of the Universe had caused the temperature to drop significantly and this reaction was "turned off". Since the Universe continued to cool down, no further fusion reactions were possible. Hence the Big Bang cosmology can account for the fact that the composition of most stars and interstellar matter is about 75% hydrogen and 25% helium. Also, the early Universe may have produced some of the nuclei of atomic numbers 3, 4, and 5 that we see today. However, NONE of the elements heavier than atomic number 5 (boron) could have been made in the early Universe; basically, it cooled and expanded too rapidly. That reali- zation led Hoyle and others to the study of stellar interiors as the only place where heavy elements can be manufactured. Thus the inability of cosmology to account for the heavy elements led directly to a better understanding of stellar evolution. Finally, what do we mean by an "open" or "closed" Universe? We need to determine the average density of matter in the Universe (at least in our part of it) in order to decide whether the Universe has enough gravity to eventually halt the expansion and turn it into a contraction. Consider how the average density might be estimated, and why is this such a difficult observational problem. -- Robert F. Wing March 6, 2001