1 Chapters 26 and 27 COSMOLOGY AND THE EARLY UNIVERSE These notes cover material that will appear on the last exam: Fri Dec 3. [Note: these notes and the lectures cover chapters 26 and 27 together, with topics discussed in a slightly different order than in the textbook. References to textbook sections and pages and figures are given below. These notes will be of most benefit if you have already read chapters 26 and 27. This material is probably the most difficult, and also the most interesting, of the entire course, so you will have to read very carefully. Because of the amount of the material, I will not test you on the “Discovery” or “More Precisely” sections of your text for these two chapters, but I suggest that you read them anyway, since they may enhance your understanding of the rest of the material.] The diagram below illustrates what we will be interested in from an observational point of view—we want to see the universe in the distant past by looking far away. By the end of this section of the course you should be able to look back at this diagram and be able to explain it in your own words. Here is a brief outline of the progression of topics. At first we will primarily be interested in observations of more and more distant galaxies (to get the “Hubble constant”), and counting up all the mass of matter we can (and can’t) see in order to find what kind of space-time universe we live in (expanding eternally? slowing down and reversing itself in the future?). The biggest recent development in this probing of larger and larger distances is the evidence that no only is there dark matter, there is some invisible, massless, energy field that is repulsive, effectively an anti-gravity force, whose nature is unknown, although later we will see that we can estimate what fraction of the universe it comprises very accurately.This is called “dark energy” and remains an enigma today.2 Then we will see that the “big bang” has provided us with several ways to probe very early times, when the universe was only 100,000 yr old (the cosmic background radiation), and even a few minutes old (the formation of deuterium and helium, whose abundance can’t be explained by formation in stars). Surprisingly, there are a number of ways in which the cosmic background radiation (relic radiation from a time when the universe was young) has provided even better estimates of cosmological quantities, like the Hubble constant and the mass density of the universe, than we can obtain by observing galaxies. Then (ch. 27) we try to go back to extremely small times, finding that the spacetime of the universe probably underwent a fantastic but theoretically reasonable kind of phase transition (think of water turning into ice) called “inflation” when it was only a tiny fraction of a second old. Your job is to try to understand how this idea of inflation all at once makes sense out of a number of observational features of our universe that previously were not accounted for. Finally, as we try to understand the stages of the universe that are inaccessible to present-day physics (quantum-gravity), we will discuss suggestions that a physically sound theory of spacetime may be one in which the universe has many more dimensions than three, that the big bang could really have been the interaction of universes in a higher-dimensional “hyperuniverse”, and even more speculative and bizarre ideas. A more detailed account begins on the next page… The Expanding Universe: The Big Bang [Sec. 26.2] Cosmology = study of the structure and evolution of the universe as a whole. Stars, galaxies, clusters of galaxies, are just “tracers” of the structure of spacetime. Comologists are interested in the structure of this spacetime continuum and how it may have changed, what its geometry is, but for our purposes we try to keep focused on the tracers we can see in order to learn about the universe as a whole To come up such a model for the universe, theorists need to assume the cosmological principle (sec. 26.1, pp.710-711): 1. Homogeneity—the local universe looks about the same no matter where you are in it. This is same as saying: no structure on size scales larger than a small fraction of size of observable universe. (A few examples given in class.) Largest known structures ~ 200-300 Mpc : “Sloan Great Wall”—see Fig. 26.1; Pencil beam survey in Fig. 26.2. These structures are much smaller than size of observable universe (~ 5000 Mpc). [Note: Universe could be much larger, or even infinite—we just can’t see back any further in time or space.] ! So homogeneity assumption probably OK.3 2. Isotropy—no preferred direction. Universe looks the same in all directions. OK. Since these two assumptions amount to saying all places in the universe are equivalent, on large enough scales, the cosmological principle implies universe has no edge and no center (ultimate principle of mediocrity). !Hubble’s law: velocity = H0 x distance ! expanding universe. Now we can ask: How big is the universe that we can see? When did it begin? How will it end? These are questions of cosmology, questions about the universe as a whole. Although there have been other contenders over the years (the “cold big bang” and the “steady state cosmology”) we’ll see that only the “hot” big bang theory (and only a particular form of it: inflationary dark matter big bang) accounts for the observations, and does so very convincingly, but at the expense of introducing two entities whose nature is completely unknown: dark matter (already encountered in previous chapters) and dark energy. The universe appears to be expanding today, so in the past everything was closer together. How long ago were all galaxies (and everything else) in the same place? Time = distance/velocity = d/(H0 x d) = 1/H0 ~ 15 billion years This is when the “big bang” must have occurred; i.e. it is the age of the universe. (Actually the age is a little different than the above estimate because the universe hasn’t been expanding at constant speed.) Note that this age is consistent with the age of the oldest objects whose age we can determine in our Galaxy, the globular clusters. This means our Galaxy was formed early in the history of the universe. ! Olbers’ paradox: why is the night sky dark instead of as bright as the surface of a star?
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