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The Principle of Mediocrity VILENKIN: WHITROW LECTURE The Principle of Mediocrity For the 2011 RAS Whitrow Lecture, Alexander Vilenkin discusses the new cosmological worldview in which much of the universe is in a state of constant accelerated expansion, called inflation, and we live on one of the many bubbles with diverse properties that are constantly being formed. What is the origin of this worldview, its possible observational tests, and its implications for the beginning and the end of the universe? he universe as we know it originated in picture – the structure of the universe beyond a great explosion that we call the Big The Whitrow Lectures our cosmic horizon. TBang. For nearly a century cosmologists The Whitrow Lectures were established The end of inflation is triggered by quantum, studied the aftermath of this explosion: how the thanks to a legacy from Gerald Whitrow, probabilistic processes and does not occur every- universe expanded and cooled down, how gal- who died in 2000. Prof. Whitrow’s career where at once. Regions where false vacuum axies were gradually pulled together by gravity, spanned astrophysics, cosmology, and decays somewhat later are “rewarded” by a etc. The nature of the Big Bang itself came into the history and philosophy of time, and larger inflationary expansion, so false vacuum focus only relatively recently. It is the subject of he worked hard to ensure that science regions tend to multiply faster than they decay. the theory of inflation, which was developed reached as wide an audience as possible. In our cosmic neighbourhood inflation ended in the early 1980s by Alan Guth, Andrei Linde The Whitrow Lectures cover topics 13.7 billion years ago, but it probably still con- and others, and has led to a radically new global in cosmology, usually with particular tinues in remote parts of the universe, and other picture of the universe. According to this new reference to philosophical aspects of the “normal” regions like ours are constantly being picture, remote regions beyond our horizon subject. They are normally given biennially. formed. This never-ending process is called eter- are strikingly different from what we observe nal inflation. The eternal nature of inflation is here and may even obey different laws of phys- not automatic, but it is very generic. Practically ics. Here I will discuss the origin of the new of inflation is constant, the prices would dou- all models of inflation that have been discussed worldview, its possible observational tests, and ble, say, every 10 years. Cosmic inflation is a so far predict eternal inflation. its implications for the beginning and the end lot faster than that: depending on the model, The details of false vacuum decay are model- of the universe. the doubling time can be as short as 10–37 sec- dependent; here, I will focus on models where I will start with a brief review of the theory of onds. In about 330 doubling times the size of the it occurs through bubble nucleation. The low- inflation. The key role in this theory is played by universe will grow by a factor of 10100. No mat- energy regions then appear as tiny microscopic a peculiar entity called “false vacuum”. Vacuum ter what its initial size is, the universe will very bubbles and immediately start to grow, at a is just empty space, but according to modern quickly become huge. Because the false vacuum rate rapidly approaching the speed of light. particle physics it is very different from “noth- is unstable, it eventually decays, producing a hot The bubbles keep growing without bound; in ing”. It is a physical object, endowed with energy fireball, and that’s the end of inflation. The fire- the meantime they are driven apart by the infla- density and pressure, and can be in a number ball continues to expand by inertia and evolves tionary expansion, making room for more bub- of different states. Particle physicists refer to along the lines of standard Big Bang cosmology. bles to form. We live in one of the bubbles and these states as different vacua. The properties Decay of the false vacuum plays the role of the can observe only a small part of it. No matter and the types of elementary particles differ from Big Bang in this scenario. how fast we travel, we cannot catch up with the one vacuum to another. The gravitational force The theory of inflation explained some other- expanding boundaries of our bubble, so for all induced by a false vacuum is rather peculiar: it is wise mysterious features of the Big Bang, which practical purposes we live in a self-contained repulsive. The higher the energy of the vacuum, simply had to be postulated before. It explained bubble universe. An unlimited number of bub- the stronger is the repulsion. The word “false” the expansion of the universe (it is due to the bles will be formed in the course of eternal infla- refers to the fact that this kind of vacuum is repulsive gravity of the false vacuum), its high tion. (For a review of inflation, including eternal unstable. It decays into a low-energy vacuum temperature (due to the high energy density of inflation, see, e.g. Guth and Kaiser 2005.) like ours, and the excess energy goes to produce the false vacuum), and its observed homogeneity a hot fireball of particles and radiation. I should (false vacuum is very homogeneous: apart from A metaphysical interlude emphasize that false vacua with these strange quantum fluctuations, it has a constant energy At this point I would like to mention a remark- properties were not invented for the purposes of density). The theory has also made a number able and, to my mind, somewhat disturbing inflation: their existence follows from particle of testable predictions. It predicted that on the consequence of this picture of the universe (Gar- physics and General Relativity. largest observable scales the universe should be riga and Vilenkin 2001). Because the number The theory of inflation assumes that at some accurately described by flat, Euclidean geom- of bubble universes is unlimited, and each of early time in its history the universe was in the etry. It also predicted a nearly scale-invariant them expands without bound, they will con- state of a high-energy false vacuum. Why it spectrum of small Gaussian density perturba- tain an unbounded number of regions of the should be so is a good question, and I will have tions. These predictions have been spectacularly size of our horizon. In each of these regions, something to say about it later in this article. confirmed by observations. By now inflation has the initial conditions at the Big Bang are set by The repulsive gravitational force produced by become the leading cosmological paradigm. random quantum processes during inflation, that vacuum would then cause a super-fast, so all possible initial conditions will be realized exponential expansion of the universe. There Eternal inflation with some probability. is a characteristic time – the doubling time – in Now that the theory of inflation is supported Now, the key point is that the number of dis- which the size of the universe would double. by the data in our observable region, we should tinct states in which any such region can be is This is similar to economic inflation: if the rate have some trust in what it tells us about the big finite. How is this possible? I can, for example, A&G • October 2011 • Vol. 52 5.1 VILENKIN: WHITROW LECTURE move my chair by one centimetre, by half a cen- 10500 (Lerche et al. 1987, Bousso and Polchinski no-one is there to complain about that. (For a timetre, by a quarter of a centimetre, and so 2000). Each solution corresponds to a vacuum non-technical review of multiverse ideas, see on, and apparently I have an infinite number of with its own types of elementary particles and Vilenkin 2006, Susskind 2006, Greene 2011.) possible states right there – because I can move its own values for the constants of Nature. Some of my colleagues find the multiverse it by an infinite number of possible displace- Now combine this with the theory of infla- theory alarming. Any theory in physics stands ments which get smaller and smaller. However, tion. Wherever they occur in the universe, high- or falls depending on whether its predictions states that are too close to one another cannot energy vacua will drive exponential inflationary agree with the data. But how can we verify be distinguished, even in principle, due to the expansion. Transitions between different vacua the existence of other bubble universes? Some quantum uncertainty. So quantum mechanics will occur through bubble nucleation, so there distinguished cosmologists, such as Paul Stein- tells us that the number of distinct states (in a will be bubbles within bubbles within bubbles. hardt and George Ellis, have even argued that finite volume) is finite. The number of quan- Each bubble type has a certain probability of the multiverse theory is unscientific, because it tum states in our observable region has been forming in the inflating space. So, inevitably, cannot be tested, even in principle. estimated as N ~ exp(10122). This is an unimagi- an unlimited number of bubbles of all Surprisingly, observational tests of nably large number. But the important point is possible types will be formed in The the multiverse picture may in fact that it is not infinite. the course of eternal inflation. be possible. One possibility is Thus, we have a finite number of states occur- This picture of the universe, constants‘‘ of to look for observational sig- ring in an infinite number of regions.
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