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CHAPTER 16 String Theory and Cosmology
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and cools with its dynamics evolving according to Einstein s equations. Interestingly, the universe exhibits a great deal of uniformity on large scales that the standard bigbang model is hard pressed to explain. To understand the type of uniformity we are talking about, we can think of everyday life. Imagine heating a cup of tea in the microwave and then taking it out and setting it on the counter. Over time, the cup of tea will cool and if we leave it there long enough, it will reach an equilibrium point where it is the same temperature as its surroundings. The same kind of behavior has occurred on the largest scales of the universe. If we examine the universe on large scales where we divide it up into cubes that have sides which are on the order of hundreds of millions of light years across, we nd Homogeneity: On large scales on the average the universe is the same everywhere. That is each cube has the same galaxy density, the same mass density, and the same luminosity. Isotropy: We have already mentioned that standard cosmology assumes the universe is isotropic, or the same in every direction. Observation bears this out to an incredibly high degree. The problem with standard big-bang theory and these observations is that the universe evolved too quickly for equilibrium in the sense we described with the cup of tea, could have occurred. There would not have been enough time for light signals to connect different spatial regions, so how could they have communicated so as to end up in exactly the same con guration Another problem with standard big-bang cosmology is known as the atness problem. The universe is at and the mass density of the early universe was apparently so exactly ne-tuned to give the observed atness that it is hard to imagine how this could be coincidence. The critical mass density is de ned in terms of the Hubble constant:
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(16.3)
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where G is Newton s gravitational constant. Now de ne =
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(16.4)
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where r is the actual mass density in the universe. Now let be the cosmological constant. If + 3H 2 (16.5)
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String Theory Demysti ed
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exceeds 1, then the universe is a closed space like a sphere. If it is less than one, then it is an open space with negative curvature (like a saddle). If it is exactly 1, then the universe is a at open space. Observation indicates that the universe is a at open space, so the atness problem boils down to the equation of why early conditions in the universe xed the mass density so close to the critical mass density. The issues which cannot be explained by classical physics-homogeneity, isotropy, and the atness problem can be explained by a theory known as in ation. This is a theory that proposes that the early universe went through a brief phase of exponential expansion. Just prior to the phase of exponential expansion, all regions of the universe were causally connected. This explains the homogeneity and isotropic problems. The expansion is driven by a scalar eld f (a quantum eld called the in aton) which has negative pressure. This acts like a repulsive gravitational eld causing different regions of the universe to repel one another and to expand outward. The in aton eld is believed to have a false vacuum, which is a metastable point that is higher in energy than the true vacuum (the lowest energy state). For a brief period, the in aton was at the false vacuum and could cause in ation, then it rolled down the hill to the true vacuum or lowest energy state. During the expansion, the total energy of the universe remains constant (as it must). During in ation, the energy of matter, which is positive, is increasing exponentially. Energy from the in aton eld can be used to actually create matter through Einstein s equation E = mc 2. As matter is added to the universe, the gravitational eld gets larger as well. The gravitational eld has negative energy density. So the increasing negative energy of the gravitational eld balances out the increasing positive energy of matter keeping the total energy of the universe constant. Quantum uctuations in the in aton eld when the universe was very small are believed to have magni ed during the exponential expansion providing seedlike structures for the universe as a whole. These seeds led to the formation of the galaxies. This is an amazing connection between quantum theory and the large-scale structure of the universe. In ation theory makes several predictions that are consistent with observation to date.