String Theory Demystified

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CHAPTER 16 String Theory and Cosmology Conventional cosmology, which grew out of general relativity, astrophysics, and quantum fi eld theory, proposes that the universe began with a “big bang” at a fi nite time in the past with an infl ationary rush, and will expand forever until the universe dies with a whimper, as a result of increasing entropy eventually sapping the useful life out of it. Proposals which originated in string/M-theory have led to different cosmological models. These models have the unexpected and shocking ability to describe the universe before the big bang. Based on a brane-world-type universe, they involve the collision of two branes which get rid of the “singularity” of bigbang theory and replace it with an eternal universe, which could be described as “cyclic.” In this chapter, we give an overview of some of the cosmological models that have arisen from string/M-theory. Unfortunately, the details of these models using string/M-theory are well beyond the scope of this book, so our description will be more of a qualitative nature. The motivated reader is urged to consult the references for details. Cosmology is sure to be an active area of research in the coming years with many new and possibly unexpected developments. Copyright © 2009 by The McGraw-Hill Companies, Inc. Click here for terms of use.
266 String Theory Demystifi ed Einstein’s Equations Infl ation In the previous chapter we introduced the Einstein fi eld equations, which give a classical description of gravity. In this chapter, we discuss the application of the Einstein fi eld equations to cosmology. For a detailed description of the study of cosmology in the context of general relativity, please see Relativity Demystifi ed and any of the references contained therein. Cosmology is the study of the evolution of the universe as a whole. The starting point is the Robertson-Walker metric: 2 2 2 2 ds =− dt + a () t dΣ (16.1) Here, dΣ 2 represents the spatial part of the metric. The function at () is called the scale factor. It characterizes the spatial size of the universe and how it changes with time. The Hubble constant is given by H a = a (16.2) We can characterize the spatial structure of the universe by a curvature constant K. If the space is fl at, has negative curvature (a saddle) or has positive curvature (a sphere), then K = 0, − 1, + 1, respectively. Observational evidence indicates that our universe is fl at. The behavior of the universe with time is determined by starting with a given metric believed to describe the overall structure of the universe, and then using it to work out the components of the curvature tensor. Then we can solve the Einstein fi eld equations either with or without matter present. This can also be done with or without a cosmological constant. In standard cosmology treatments, space is assumed to be isotropic, meaning that it is the same in all directions. We may not want to make that assumption in string theory where some spatial dimensions are treated differently. There are two cosmological models that come up rather repeatedly. A de Sitter universe is one without matter (a vacuum solution of Einstein’s fi eld equations), with fl at space, and a positive cosmological constant. An anti-de Sitter universe (sometimes denoted AdS) is a vacuum solution to the Einstein fi eld equations with positive cosmological constant and negative scalar curvature. The cosmological models studied in relativity theory are only a part of modern cosmology. The second piece which is needed to explain known data is infl ation. The standard big-bang model begins the universe with a singularity and it expands
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Accounting Demystified Advanced Cal
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Copyright © 2009 by The McGraw-Hil
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Contents vii BRST in String Theory-
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Contents ix CHAPTER 14 Black Holes
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PREFACE String theory is the greate
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Preface xiii time as this one to he
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CHAPTER 1 Introduction General rela
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CHAPTER 1 Introduction 13 Figure 1.
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CHAPTER 1 Introduction 15 • Type
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CHAPTER 1 Introduction 17 Close up,
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CHAPTER 1 Introduction 19 5. The mi
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CHAPTER 2 The Classical String I: E
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CHAPTER 2 Equations of Motion 23 To
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CHAPTER 2 Equations of Motion 25 No
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CHAPTER 2 Equations of Motion 29 ct
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CHAPTER 2 Equations of Motion 31 Th
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CHAPTER 2 Equations of Motion 37 ho
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CHAPTER 2 Equations of Motion 39 Th
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CHAPTER 2 Equations of Motion 41 wh
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CHAPTER 2 Equations of Motion 43 In
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CHAPTER 2 Equations of Motion 47 We
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CHAPTER 2 Equations of Motion 49 In
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CHAPTER 3 The Classical String II:
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CHAPTER 3 Symmetries and Worldsheet
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CHAPTER 4 String Quantization At th
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CHAPTER 4 String Quantization Here,
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CHAPTER 4 String Quantization That
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CHAPTER 4 String Quantization Using
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CHAPTER 4 String Quantization expec
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CHAPTER 4 String Quantization † A
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CHAPTER 4 String Quantization To ob
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CHAPTER 4 String Quantization lower
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CHAPTER 4 String Quantization this)
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CHAPTER 4 String Quantization Norma
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CHAPTER 5 Conformal Field Theory Pa
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CHAPTER 6 BRST Quantization So far
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CHAPTER 6 BRST Quantization 121 The
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CHAPTER 6 BRST Quantization 123 To
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CHAPTER 6 BRST Quantization 125 The
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CHAPTER 7 RNS Superstrings The real
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CHAPTER 7 RNS Superstrings 129 EXAM
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CHAPTER 7 RNS Superstrings 131 SOLU
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CHAPTER 7 RNS Superstrings 133 In t
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CHAPTER 7 RNS Superstrings 135 Now,
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CHAPTER 7 RNS Superstrings 137 We c
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CHAPTER 7 RNS Superstrings 139 We o
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CHAPTER 7 RNS Superstrings 141 OPEN
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CHAPTER 7 RNS Superstrings 143 If w
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CHAPTER 7 RNS Superstrings 145 The
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CHAPTER 7 RNS Superstrings 147 From
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CHAPTER 7 RNS Superstrings 151 3. A
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CHAPTER 8 Compactifi cation and T-D
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CHAPTER 9 Superstring Theory Contin
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CHAPTER 10 A Summary of Superstring
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CHAPTER 11 Type II String Theories
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CHAPTER 12 Heterotic String Theory
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Page 254 and 255: CHAPTER 14 Black Holes Black holes,
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Page 264 and 265: CHAPTER 14 Black Holes 249 Entropy
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Page 312 and 313: Books References Becker, K., M. Bec
Page 314 and 315: |NS〉 ⊕ |NS〉 Sector, 203 |NS
Page 316 and 317: INDEX 301 Cyclic model, 277 Cylinde
Page 318 and 319: INDEX 303 Mechanics, quantum. See Q
Page 320 and 321: INDEX 305 Schwarzschild metric, 242
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String Theory Demystified

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