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Authors: Alex Vilenkin

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To: Galactic Council
From: WSX–23EDJ
 
Greetings! As required by the Protocol, I have completed my inspection of the planet Earth, located in sector S—16 in the peripheral zone of the Galaxy. The human race populating this planet has made good progress in the 1000 Earth years since the last inspection. I have upgraded their status from “budding” to “technologically challenged.”
You will be amused to know that humans believe they are close to discovering the final theory of the universe. I envy their youthful enthusiasm … On certain issues they have come close to the right answers—surprisingly, I would say, for a primitive civilization such as this. In other matters, though, they are pretty far behind. They have not even figured out the right questions.
Overall, this race is still rather immature. I recommend against inclusion in the Galactic Union at this time. Further details will be forthcoming in my regular report.
 
Yours respectfully,
WSX—23EDJ
1. WHAT BANGED, HOW IT BANGED, AND WHAT CAUSED IT TO BANG
1
A. H. Guth,
The Inflationary Universe
(Addison-Wesley, Reading [Mass.], 1997, p. 2).
 
2. THE RISE AND FALL OF REPULSIVE GRAVITY
1
Einstein to Ehrenfest, January 16, 1916 (as quoted in A. Pais,
Subtle is the Lord
(Oxford University Press, Oxford, 1982).
2
Einstein to Sommerfeld, February 8, 1916, ibid.
3
It was later realized that Einstein’s static cosmological model is not acceptable even on purely theoretical grounds, because the balance between attractive and repulsive gravity in this model is unstable. If for some reason the size of the universe is slightly increased, the matter density will go down (since the distances between galaxies will grow), while the vacuum energy density will remain the same, being fixed by the cosmological constant. Hence, the repulsive gravity of the vacuum will now be stronger than the attractive gravity of matter and will cause the universe to expand. This will lead to a further increase of volume and to even greater imbalance between the attractive and repulsive forces. The universe will thus enter a regime of runaway expansion. Similarly, if the size of Einstein’s static universe is slightly decreased, the attractive gravity of matter will win over the repulsion of the vacuum and the universe will collapse to a point. Small fluctuations in the size of the universe are inevitable according to the quantum theory, and thus Einstein’s universe cannot remain in balance for an infinite time.
 
3. CREATION AND ITS DISCONTENTS
1
As quoted in E. A. Tropp, V.Y. Frenkel, and A. D. Chernin,
Aleksandr Aleksandrovich Fridman
(Nauka, Moscow, 1988, p. 133).
2
Friedmann did not consider the case of a spatially flat universe. It was studied by Einstein and Willem de Sitter in 1932.
3
A notable exception was Einstein’s reaction to Friedmann’s work. Initially, Einstein thought that Friedmann had made a mistake and wrote a brief note to the journal pointing to what he thought was an error. However, in less than a year he had to withdraw his criticism after a conversation with Friedmann’s friend, Yuri Krutkov. Krutkov reported home that he had won a debate with Einstein and that “Petrograd’s honor is saved!” But Einstein, though he agreed with Friedmann’s mathematics, still believed that the universe was static and that Friedmann’s work was therefore of purely formal interest. In his second note to the journal, he wrote that he was “convinced that Mr. Friedmann’s results are both correct and clarifying.” He added in the original draft that the results could hardly be of any physical significance, but then crossed this phrase out, perhaps realizing that it was based more on his philosophical prejudice than on any known fact. Quotes are from Helge Kragh,
Cosmology and Controversy
, (Princeton University Press, Princeton [N.J.], 1996).
4
The source of stellar energy was not known in Helmholtz’s time, but now we know that stars are burning nuclear fuel by turning hydrogen into helium and then into heavier nuclei. This is an irreversible process accompanied by an increase of entropy, and eventually stars run out of nuclear fuel. Some stars turn off their nuclear engines without much fanfare and then gradually cool down, while others explode, throwing their constituent gas into the interstellar space and leaving behind a compact remnant (a neutron star or a black hole). The expelled gas can be reprocessed to form new stars, but sooner or later the gas supply will be exhausted, as more and more of it ends up in cold stellar remnants. In a trillion years from now, galaxies will probably be noticeably dimmer than they are today. The process of gradual dimming of lights may be rather protracted, but one thing is clear: the universe as we know it could not have existed forever.
5
Boltzmann’s fluctuation idea is probably the first example of what will later be known as
anthropic arguments
(see Chapter 13).
6
The first persuasive evidence for the galactic evolution was presented in the 1950s by the Cambridge astronomer Martin Ryle. He found that powerful radio emission from galaxies was much more common a few billion years ago than it is now.
7
Arthur Conan Doyle,
The Sign of Four
.
 
4. THE MODERN STORY OF GENESIS
1
Quoted from R. H. Stuewer, in
The Kaleidoscope of Science
, ed. by E. Ullmann-Margalit (Reidel, Dordrecht [Netherlands], 1986, p. 147).
2
The description of Gamow’s life in this section is based mostly on his unfinished autobiography,
My World Line
(Viking Press, New York, 1970).
3
Atoms are made of small, positively charged nuclei and negatively charged electrons “orbiting” around them. (I put “orbiting” in quotation marks, because quantum uncertainties are important in the atom, so instead of picturing electrons as moving in
an orderly way along their orbits, like planets around the Sun, it is more accurate to picture them as being “smeared” around the orbits.) The nuclei consist of two types of subatomic particles: protons, which have a positive electric charge, and neutrons, which are electrically neutral. The chemical properties of an atom are determined solely by the number of electrons (which is equal to the number of protons, so that the atom is electrically neutral).
4
The origin of this imbalance between matter and antimatter is one of the active areas of research in modern cosmology. For a discussion, see A. H. Guth,
The Inflationary Universe
(Addison-Wesley, Reading [Mass.], 1997).
5
A more detailed discussion of the hot fireball and element formation can be found in Steven Weinberg’s classic bestseller
The First Three Minutes
(Bantam, New York, 1977).
6
M. J. Rees,
Before the Beginning
(Addison-Wesley, Reading [Mass.], 1997, p. 17).
7
S. Weinberg, op. cit., p. 123.
 
5. THE INFLATIONARY UNIVERSE
1
The twists and turns of Alan Guth’s path to the discovery of inflation are described in his excellent book
The Inflationary Universe: The Quest for a New Theory of Cosmic Origins
(Addison-Wesley, Reading [Mass.], 1997).
2
It is conceivable that our vacuum is not, in fact, the lowest-energy one. String theory, which is now the prime candidate for the fundamental theory of nature, suggests the existence of negative-energy vacua. If they do exist, then our vacuum may eventually decay, with catastrophic consequences for all the material objects it contains. We shall discuss string theory in Chapter 15 and the possibility of our vacuum decay in Chapter 18. Until then we shall assume that we live in the true vacuum.
3
This conclusion is easy to understand from simple energy considerations. The force on a physical object always acts in the direction of reducing its energy (more precisely, its
potential
energy, that is, the part of energy not related to motion). For example, the force of gravity pulls objects down, so that their energy is decreased. (The gravitational energy grows with elevation above the ground.) For a false vacuum, the energy is proportional to the volume it occupies and can be reduced only by reducing the volume. Hence, there should be a force causing the vacuum to shrink. This is the force of tension.
 
6. TOO GOOD TO BE WRONG
1
A. H. Guth, “The inflationary universe: A possible solution to the horizon and flatness problems,”
Physical Review
, vol. D23, p. 347 (1981).
2
The Starobinsky model is based on a modified form of Einstein’s gravitational equations. The modification becomes important only when the curvature of spacetime gets very high. The magnitude of the curvature plays the role of a scalar field in this theory.
3
True to the Russian style, Mukhanov and Chibisov wrote their paper “for Landau,”
stating their result and providing little detail of how it was derived. Some of the Nuffield participants argue that an important step may be missing in this derivation and that Mukhanov and Chibisov may not, therefore, deserve full credit for the result. In my opinion, they do.
 
8. RUNAWAY INFLATION
1
A. Vilenkin, “The birth of inflationary universes,”
Physical Review
, vol. D27, p. 2848 (1983). This paper is about quantum cosmology; eternal inflation is discussed in sections IV and V.
2
An exponentially expanding region would quickly cover the whole computer screen, forcing us to stop the simulation. We dealt with this problem by using an expanding distance scale, which grew at the same rate as the inflating regions. Measured by this expanding ruler, the size of the inflating false-vacuum volume does not change in time, so it occupies a fixed area on the screen. In the economic inflation analogy that we used in Chapter 5, this method of measurement corresponds to expressing prices in “original dollars,” so that the effect of inflation is factored out.
3
M. Aryal and A. Vilenkin, “The fractal dimension of the inflationary universe,”
Physics Letters
, vol. B199, p. 351 (1987).
4
A. D. Linde, “Eternally existing self-reproducing chaotic inflationary universe,”
Physics Letters
, vol. B175, p. 395 (1986). The term “eternal inflation” was introduced by Linde in this paper.
 
9. THE SKY HAS SPOKEN
1
The accelerated expansion of the universe was discovered by the High-Redshift Supernova Search Team, led by the Harvard astronomer Robert Kirshner and by Brian Schmidt of Siding Springs Observatory in Australia, and by the Supernova Cosmology Project team, led by Saul Perlmutter. For a witty firsthand account of this discovery, see Robert Kirshner’s book
The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos
(Princeton University Press, Princeton, [N.J.], 2004).
2
Inflation can be reconciled with density smaller than critical at the expense of making the theory more complicated and less attractive. To this end, the scalar field energy landscape needs to be specially designed. It needs to have a barrier, as in Guth’s original model (
Figure 6.2
). But instead of dropping steeply toward the minimum, the barrier must be followed by a very gentle slope. The resulting model combines the features of Guth’s old inflation scenario with the improved scenario by Linde and others. The field tunnels through the barrier via bubble nucleation and completes its journey to the minimum by slowly rolling downhill within individual bubbles. In his analysis of vacuum bubbles, Sidney Coleman showed that from within they look like open Friedmann universes with density smaller than critical. By carefully adjusting the height and the slope of the hill, one can arrange for the density to be close, but not too
close, to the critical density. Physicists find such fine-tuning very distasteful, so the hope is that it will not be needed.
If, on the other hand, observations point to a density greater than critical, by more than one part in 100,000, the implication would be that the universe is a relatively small three-dimensional sphere, not much larger than the present horizon. This would pose a severe problem for inflation.
3
The origin of gravitational waves is similar to that of the density perturbations (see Chapter 6). They are produced as quantum fluctuations during inflation, with amplitudes independent of their length scale. The prediction of gravitational waves follows from the work that Alexei Starobinsky did in 1980, before Guth proposed the idea of inflation.
4
Clover will start operating in 2008. It will be able to detect gravitational waves from inflation only if the false vacuum had a grand-unification energy scale. For a lower-energy vacuum, a more sensitive instrument will be needed.
 
10. INFINITE ISLANDS
1
A. D. Linde, “Life after inflation,”
Physics Letters
, vol. B211, p. 29 (1988).
2
In flat spacetime, the square of the interval between two events is defined as (time separation)
2
– (space separation)
2
. Except for the minus sign, this quantity is very similar to the length squared in the Pythagorean theorem. To calculate the interval, time and space separations have to be expressed in compatible units. For example, if time is measured in years, then length should be measured in light-years. The interval is timelike if its square is positive, and is spacelike if it is negative. For the class reunion and superball events discussed in the text, the time separation is 3 years, the space separation is 4 light-years, so the interval squared is 3
2
– 4
2
= –7. Hence, the interval is spacelike.
BOOK: Many Worlds in One: The Search for Other Universes
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