String Cosmology: Modern String Theory Concepts from the Big Bang to Cosmic Structure 1st Edition by Johanna Erdmenger (PDF)

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This relatively new field applies equations from string theory to solve the questions of early cosmology, since the standard picture of our universe emerging from a ‘big bang’ leaves many fundamental issues unanswered. String theory, on the other hand, postulates that fundamental ingredients of nature are not zero-dimensional point particles but tiny one-dimensional filaments. This theory harmoniously unites quantum mechanics and general relativity — the previously known laws of the small and the large — which are otherwise incompatible. The field of string cosmology has matured considerably over the past few years, attracting many new adherents. Due to the multidisciplinary nature of the topic, it is difficult for practitioners to be conversant with all the many different aspects. This book thus fills a huge gap by bringing together all the different strains of research into one single volume. The resulting collection of selected articles presents the latest, ongoing results from renowned experts currently working in the field. From the contents: * Introduction to Cosmology and String Theory * String Inflation: Brane Inflation and Inflation from Moduli * Cosmic Superstrings * The CMB as a Possible Probe of String Theory * String Gas Cosmology * Gauge-gravity Duality and String Cosmology * Heterotic M-theory and C A welcome addition to the literature for graduate students, students in astronomy, astronomers, mathematicians and theoretical physicists.

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Editorial Reviews: From the Inside Flap This relatively new field applies equations from string theory to solve the questions of early cosmology, since the standard picture of our universe emerging from a ‘big bang’ leaves many fundamental issues unanswered. String theory, on the other hand, postulates that fundamental ingredients of nature are not zero-dimensional point particles but tiny one-dimensional filaments. This theory harmoniously unites quantum mechanics and general relativity — the previously known laws of the small and the large — which are otherwise incompatible. The field of string cosmology has matured considerably over the past few years, attracting many new adherents. Due to the multidisciplinary nature of the topic, it is difficult for practitioners to be conversant with all the many different aspects. This book thus fills a huge gap by bringing together all the different strains of research into one single volume. The resulting collection of selected articles presents the latest, ongoing results from renowned experts currently working in the field. From the contents: * Introduction to Cosmology and String Theory * String Inflation: Brane Inflation and Inflation from Moduli * Cosmic Superstrings * The CMB as a Possible Probe of String Theory * String Gas Cosmology * Gauge-gravity Duality and String Cosmology * Heterotic M-theory and C A welcome addition to the literature for graduate students, students in astronomy, astronomers, mathematicians and theoretical physicists. From the Back Cover This relatively new field applies equations from string theory to solve the questions of early cosmology, since the standard picture of our universe emerging from a ‘big bang’ leaves many fundamental issues unanswered. String theory, on the other hand, postulates that fundamental ingredients of nature are not zero-dimensional point particles but tiny one-dimensional filaments. This theory harmoniously unites quantum mechanics and general relativity — the previously known laws of the small and the large — which are otherwise incompatible. The field of string cosmology has matured considerably over the past few years, attracting many new adherents. Due to the multidisciplinary nature of the topic, it is difficult for practitioners to be conversant with all the many different aspects. This book thus fills a huge gap by bringing together all the different strains of research into one single volume. The resulting collection of selected articles presents the latest, ongoing results from renowned experts currently working in the field. From the contents: * Introduction to Cosmology and String Theory * String Inflation: Brane Inflation and Inflation from Moduli * Cosmic Superstrings * The CMB as a Possible Probe of String Theory * String Gas Cosmology * Gauge-gravity Duality and String Cosmology * Heterotic M-theory and C A welcome addition to the literature for graduate students, students in astronomy, astronomers, mathematicians and theoretical physicists. About the Author Johanna Erdmenger is a research group leader at the Max Planck Institute for Physics, Munich, Germany. She obtained her Ph.D. degree from the University of Cambridge, England, in 1996 and spent two years as a postdoctoral fellow at MIT (Cambridge, Massachusetts, USA) from 1999-2001. She has written over 40 publications in the areas of string theory and quantum field theory, in particular on gauge/gravity dualities and their relation to QCD, on matrix cosmology, on supersymmetry breaking and on field theory methods in condensed matter theory. She has recently been appointed as editor of The European Physical Journal C. Excerpt. © Reprinted by permission. All rights reserved. String CosmologyJohn Wiley & SonsCopyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimAll right reserved.ISBN: 978-3-527-40862-7Chapter OneIntroduction to Cosmology and String TheoryJohanna Erdmenger and Martin Ammon1.1 Introduction Cosmology and string theory are two areas of fundamental physics which have progressed significantly over the last 25 years. Joining both areas together provides the possibility of finding microscopic explanations for the history of the early universe on the one hand, and of deriving observational tests for string theory on the other. In the subsequent seven chapters, different aspects of string cosmology are introduced and discussed. This chapter contains a summary of the basics of both cosmology and string theory in view of providing a reference and glossary for the subsequent chapters. The basic concepts are introduced and briefly described, emphasizing those aspects which are used in the remainder of this book. There is a wealth of excellent textbooks of both cosmology and string theory, to which readers interested in further details are referred to – for example. Reviews on string cosmology include. An introduction to string cosmology is found in the textbook. Cosmology is introduced in Sections (1.2)–(1.4) below, and string theory in Sections (1.5)–(1.11). 1.2 Foundations of Cosmology On the basis of experimental evidence, the common scenario of present-day cosmology is the model of the hot big bang, according to which the universe originated in a hot and dense initial state 13.7 billion years ago, and then has expanded and is still expanding. The most essential feature of the present-day universe is that it is homogeneous and isotropic, that is its structure is the same at every point and in every direction. This “standard model of cosmology” has received substantial experimental backup, beginning with the discovery of the cosmic microwave background (CMB) radiation by Penzias and Wilson in 1964. In recent years, a wealth of precise data has been collected. We list just a few of the important new observations here: In the 1990s, observations of galaxies with the Hubble Space Telescope led in particular to an accurate measurement of the Hubble parameter. Fluctuations in the cosmic microwave background radiations have been observed with the COBE satellite, and subsequently with the BOOMERanG experiment. A further increase in precision came with the WMAP satellite launched in 2001, whose measurements of the parameters of the standard model of cosmology are consistent with the conclusion that the present-day universe is flat. Moreover, these measurements support the scenario of cosmic inflation. They will be supplemented by further data from the PLANCK satellite in the near future. 1.2.1 Metric and Einstein Equations The homogeneity and isotropy of the universe is best described by the Robertson Walker metric, which in (-, +, +, +) signature commonly used in string theory reads [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1.1) Here a(t) describes the relative size of space-like hypersurfaces at different times. κ = +1, 0, -1 stands for positively curved, flat, and negatively curved hypersurfaces, respectively. The frequency of a photon traveling through the expanding universe experiences a redshift z of the size [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.2) where λ denotes the photon wavelength. Using the scale factor a(t) we define the Hubble parameter H [equivalent] a/a, (1.3) with a(t) = da/dt. As was first discovered and suggested by Edwin Hubble, and has been verified with high precision by modern observational methods, the most distant galaxies recede from us with a velocity given by the Hubble law, v [congruent to] Hd, (1.4) where d is the distance between us and the galaxies considered. For describing the expanding universe it is often useful to use the term e-foldings, defined as e [equivalent] ln(a(tf)/a(ti)), which describes the growth of the scale factor between some time ti and a later time tf. The dynamics governing the evolution of the scale factor a(t) are obtained from inserting the Robertson–Walker metric into the Einstein equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.5) where Rμv and R are the Ricci tensor and scalar, G the Newton constant, and Tμv the energy–momentum tensor. The universe is best described by the perfect fluid form for the energy–momentum tensor of cosmological matter, given by Tμv = ([??] + p)uμuv + pgμv, (1.6) where uμ is the fluid four-velocity, [??] is the energy density in the rest frame of the fluid, and p is the pressure in the same frame. For consistency with the Robertson Walker metric, fluid elements are comoving in the cosmological rest frame, with normalized four-velocity uμ = (1, 0, 0, 0). (1.7) The energy–momentum tensor is diagonal and takes the form [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.8) where gij stands for the spatial part of the Robertson–Walker metric, including the factor of a2(t). Inserting the Robertson–Walker metric (1.1) into the Einstein equation (1.5) with the energy–momentum tensor (1.6), we obtain the first Friedmann equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.9) with the total energy density [??] = Σj[??]j, where the sum is over all different types of energy density in the universe. Moreover, we have the evolution equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1.10) Here pj labels the different types of momenta. Equations (1.9) and (1.10) may be combined into the second Friedmann equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1.11) The first Friedmann equation may be used to define the critical energy density [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.12) for which κ = 0 and space is flat. The density ratio [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.13) thus allows us to relate the total energy density of the universe to its curvature behavior, Ωtotal > 1 [??] κ = 1, Ωtotal = 1 [??] κ = 0, Ωtotal <1 [??] κ = 1. (1.14) Recent WMAP observations have shown that today, Ωtotal = 1 to great accuracy, which leads to the conclusion that the universe is flat. Energy conservation, [for all]μTμv = 0, gives the relation [??] + 3H([??] + p) = 0. (1.15) This relation is not independent of the Friedmann equations. Using both of them, energy conservation (1.15) may be rewritten as d/dt([??]a3) = -p d/dt a3. (1.16) 1.2.2 Energy Content of the Universe There is good experimental evidence, in particular from WMAP measurements, that the cosmic fluid contains four different components, and that the total energy density [??]total in the universe is equal to the critical density [??]c given by (1.12). This implies [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.17) with Ωj denoting the present-day fraction of the energy density contributed by the j-th fluid component. The four components of the cosmic fluid are the following: 1. Radiation: this component contains predominantly photons, most of which correspond to the cosmic microwave background. The photons are thermally distributed with temperature T = 2.715 K. The gas of photons satisfies the equation of state pRad = 1/3[??]Rad. (1.18) Moreover, there are also cosmic relic neutrinos in this fluid component, thermally distributed with T = 1.9 K. The total energy density of radiation is a small fraction, ΩRad [approximately equals] 8 × 10-5, (1.19) of the total present-day energy density. 2. Baryons: since their rest mass is much larger than their kinetic energy, their equation of state is pB [approximately equals] 0. (1.20) Their energy fraction is ΩB [approximately equals] 4%. (1.21) 3. Dark Matter: observations of galaxy movement and of matter influence on fluctuations in the CMB provide evidence that there has to be a large amount of long-lived nonrelativistic matter subject to gravitation, which is not detectable by its emitted radiation. Determining the exact structure of this dark matter remains one of the essential challenges of modern cosmology. Just as for the baryons, dark matter has the equation of state pDM [congruent to] 0, (1.22) while its energy fraction is ΩDM [approximately equals] 26%, (1.23) so that the overall density of nonrelativistic matter is ΩM [equivalent] ΩB + ΩDM [approximately equals] 30%. (1.24) 4. Dark Energy: a fourth, similarly unexplained contribution to the cosmic fluid is dark energy, which for a total energy density Ω = 1, has to be present in the universe with the large fraction ΩDE [approximately equals] 70%. (1.25) Its equation of state is expected to be pDE = -[??]DE. (1.26) Observational evidence that such a fluid component with negative pressure must be present include tests of the Hubble expansion rate using supernovae which imply that the overall expansion rate of the universe, the Hubble parameter H = a/a, is increasing at present. The Friedmann equation (1.11) implies that this can only happen for positive energy density if the total pressure is sufficiently negative, p <1/3[??]. Since none of the other fluid components has negative pressure, a large fraction of such a component must be present. Each of the above equations of state implies that wj = pj/[??]j is time independent, with wRad = 1/3, wM = 0, wDE = -1. (1.27) Inserting these values into the energy conservation condition in the form (1.16) we obtain, with a0 the present-day value of a, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.28) where αRad = 4, αM = 3, αDE = 0. (1.29) The different equations of state for the different fluid components thus imply that their relative abundances differ in the past universe as compared to the present-day observations since their energy densities vary differently as the universe expands. The history of the universe splits into periods where radiation, matter, and dark energy dominate the evolution of the total density, consecutively. The transition between the radiation and matter-dominated regimes is called radiation–matter equality and occurs at a scale given by the comoving wave vector of magnitude k [congruent to] (aH)eq. Note also that the Friedmann equation (1.9) implies that for w > -1/3, the scale factor a(t) grows more slowly than the Hubble scale H-1(t). It is useful to define the comoving frame which moves along with the Hubble flow. A comoving observer is the only one which sees an isotropic universe. 1.2.3 Development of the Universe During its expansion the universe experienced a number of decisive physical events. The earliest cosmological event for which there is observational evidence is nucleosynthesis, which began about three minutes after the big bang, and lasted for about fifteen minutes. At this time, the universe cooled below 1 MeV and light nuclei, hydrogen, helium, lithium, and beryllium, began to accumulate from protons and neutrons. The observational evidence for nucleosynthesis comes from measuring the relative abundance of these elements. The radiation–matter crossover described above occurred at a redshift (1.2) of z ~ 3600, or about 50 000 years after the big bang. After this crossover, density inhomogeneities can grow only logarithmically with a while they grow linearly with a during radiation domination. At a redshift of around z ~ 1100, or about 380 000 years after the big bang, recombination of nuclei and electrons into electrically neutral atoms occurs. This is the origin of the cosmic microwave background which corresponds to the light which is free to move through the universe after recombination. Beforehand, photons interact with the charged medium surrounding them on short scales. The CMB corresponds to a surface of last scattering for the photons. Measurements of the CMB temperature fluctuations, which are of the order δT/T ~ 10-5, provide direct information about the size of primordial density fluctuations at this time. Finally, galaxy formation occurs in the universe once the primordial density fluctuations have been amplified to a scale at which they are no longer well-described by linear perturbations. According to the cold dark matter model (for reviews see for instance), the distribution of galaxies observed today also requires the presence of nonrelativistic (cold) dark matter, together with nonlinear fluctuations. 1.3 Inflation 1.3.1 Puzzles Within the Big Bang Model When considering the initial conditions characterizing matter in the big bang scenario of an expanding universe, we encounter a number of puzzles. Three of them are discussed in the subsequent text. The initial conditions fix the matter distribution in the universe at the Planckian time of tp = 10-43 s when classical gravity becomes applicable. Horizon problem. The horizon problem relates to the fact that the universe is so extremely homogeneous. The Friedmann equation (1.9) implies that the universe expands so quickly that thermal equilibration would violate causality. A dimensional analysis for the ratio ai/a0 of the initial and the present-day value of the scale factor a(t) shows that our universe was initially larger than a casual patch by a factor of the order ai/a0. If expansion was always decelerated by an attractive gravity force, which implies ai/a0 >> 1, then the homogeneity scale was always larger than the causality scale. In fact, using the present size of the universe, the Planck time and the temperature of the universe now and at Planck time, one finds that ai/a0 ~ 1028. This would require an extraordinary fine tuning. Flatness problem. While the horizon problem relates to the initial conditions for the spatial distribution of matter, the flatness problem relates to the initial velocities. These must satisfy the Hubble law (1.4). The ratio of the kinetic to the total energy of matter in the universe is again given by (ai/a0)2 and if this ratio is very large, a very unnatural fine tuning between the kinetic energy associated to Hubble expansion and the gravitational potential energy is required. This may be seen from the Friedmann equation (1.9) which implies Ω(t) – 1 = κ/(Ha)2, (1.30) and thus, since the present-day Ω0 has been observed to be very close to unity, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.31) for ai/a0 ~ 1028. Such an astonishing fine-tuning appears implausible. Initial perturbations. A third puzzle, related to the other two, concerns the origin of the original inhomogeneities needed to explain the large-scale structure of the present-day universe. 1.3.2 The Concept of Inflation A concept which can solve the puzzles mentioned is inflation. The idea of inflation, first suggested in, is that there is an initial stage of accelerated expansion where gravity acts as a repulsive force. If gravity was always positive, then ai/a0 is necessarily larger than one since gravity decelerates expansion. ai/a0 <1 is possible only if gravity is repulsive during some period of expansion. This period of repulsive gravity can in particular explain the creation of our universe from a single causally connected region. Moreover, since it accelerates expansion, small initial velocities inside a causally connected region become very large. In the inflationary period we have ã > 0. From the Friedmann equation (1.11), which may be written in the form ä = -4πG/3([??] + 3p)a, (1.32) for the total energy density [??] and the total momentum p. We read off that ä > 0 requires [??] + 3p <0. This implies that the strong energy dominance condition, [??] + 3p > 0, must be violated during inflation. One example which violates this condition is a positive cosmological constant for which p [approximately equals] -[??]. (Continues…) Excerpted from String Cosmology Copyright © 2009 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Excerpted by permission of John Wiley & Sons. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site. Read more

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Free Download String Cosmology: Modern String Theory Concepts from the Big Bang to Cosmic Structure 1st Edition in PDF format
String Cosmology: Modern String Theory Concepts from the Big Bang to Cosmic Structure 1st Edition PDF Free Download
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String Cosmology: Modern String Theory Concepts from the Big Bang to Cosmic Structure 1st Edition 2009 PDF Free Download
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