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Conformal symmetry and deflationary gas universe 257 With the expressions (30), (20), and (22), we obtain For we write where It follows that Integration of this equation yields where we have restricted ourselves to The potential is given by or, This expression was found by Maartens et al. [16] as exactly that potential which produces a cosmological dynamics of the type (22). In terms of the scalar field the cosmic evolution starts with and At the value of the potential is reduced to A scalar field description with this potential implies the same cosmological dynamics as a self–interacting gas model in which the particles self–consistently move under the influence of an effective one–particle force characterized by the second equation in (23). The above relations allow us to change from the fluid to the scalar field picture and vice versa at any time of the cosmological evolution. In principle, it is possible to “calculate” the potential if the self–interacting fluid dynamics is known. 7. CONCLUSIONS We have presented an exactly solvable gas dynamical model of a deflationary transition from an initial de Sitter phase to a subsequent radiation dominated FLRW period. The entire transition dynamics represents a specific non–equilibrium configuration of a self–interacting gas.
258 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY Although connected with entropy production, this configuration is characterized by an equilibrium distribution function of the gas particles. Macroscopically, this evolution is connected with a smooth transition from a “symmetry” condition (where is a “projector- conformal timelike Killing vector” [7]) during the de Sitter stage to the conformal symmetry as the FLRW dynamics is approached. Mapping the non-equilibrium contributions onto an effective refraction index of the cosmic matter, the deflationary transition appears as the manifestation of a timelike conformal symmetry of an optical metric in which the refraction index changes smoothly from a very large value in the de Sitter period to unity in the FRLW phase. The deflationary gas dynamics may alternatively be interpreted as a production process of relativistic particles out of a decaying vacuum. Furthermore, there exists an equivalent scalar field description with an exponential type potential which generates the same deflationary scenario as the self-interacting gas model. Acknowledgments This work was supported by the Deutsche Forschungsgemeinschaft. References [1] J.M. Stewart, Non–equilibrium Relativistic Kinetic Theory (Springer, New York, 1971). [2] J. Ehlers, in: General Relativity and Cosmology, ed. by B.K. Sachs (Academic Press, New York, 1971). [3] G.E. Tauber and J.W. Weinberg, Phys. Rev. 122 (1961) 1342. [4] N.A. Chernikov, Sov. Phys. Dokl. 7 (1962) 428. [5] W. Zimdahl, Phys. Rev. D57 (1998) 2245. [6] W. Zimdahl and A.B. Balakin, Class. Quantum Grav. 15 (1998) 3259. [7] W. Zimdahl and A.B. Balakin, Phys. Rev. D58 (1998) 063503. [8] W. Zimdahl and A.B. Balakin, Gen. Rel. Grav. 31 (1999) 1395. [9] W. Zimdahl and A.B. Balakin, Phys. Rev. D (2001) to appear. (Preprint astroph/0010630) [10] J.D. Barrow, Phys. Lett. B180 (1986) 335. [11] W. Gordon, Ann. Phys. (NY) 72 (1923) 421. [12] J. Ehlers, Z. Naturforschg. 22a (1967) 1328. [13] V. Perlick, Ray Optics, Fermat’s Principle, and Applications to General Relativity (Springer, Berlin, 2000). [14] J.A.S. Lima and J.M.F. Maia, Phys. Rev. D49 (1994) 5597. [15] E. Gunzig, R. Maartens, and A.V. Nesteruk, Class. Quantum Grav. 15 (1998) 923; A.V. Nesteruk, Gen. Rel. Grav. 31 (1999) 983.
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EXACT SOLUTIONS AND SCALAR FIELDS I
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EXACT SOLUTIONS AND SCALAR FIELDS I
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To the 65th birthday of Heinz Dehne
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CONTENTS Preface Contributing Autho
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Contents ix 5 The case of 84 Part I
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Contents xi Luis O. Pimentel, Cesar
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Contents xiii 2.2 String theory ind
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PREFACE This book is dedicated to h
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CONTRIBUTING AUTHORS Eloy Ayón-Bea
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Contributing Authors xix Jaime Klap
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Contributing Authors xxi A.P. 70-54
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Contributing Authors xxiii L. Artur
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I EXACT SOLUTIONS
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SELF-GRAVITATING STATIONARY AXI- SY
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Self-gravitating stationary axisymm
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REFERENCES 13 be shown that the ana
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NEW DIRECTIONS FOR THE NEW MILLENNI
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New Directions for the New Millenni
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New Directions for the New Millenni
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REFERENCES 21 Acknowledgments The r
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ON MAXIMALLY SYMMETRIC AND TOTALLY
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On maximally symmetric and totally
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DISCUSSION OF THE THETA FORMULA FOR
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Theta formula for the Ernst potenti
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REFERENCES 51 Rosenhain’s theta f
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THE SUPERPOSITION OF NULL DUST BEAM
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The superposition of null dustbeams
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REFERENCES 61 geodesic with respect
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SOLVING EQUILIBRIUM PROBLEM FOR THE
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Solving equilibrium problem for the
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REFERENCES 67 where the subindices
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ROTATING EQUILIBRIUM CONFIGURATIONS
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Rotating equilibrium configurations
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Rotating equilibrium configurations
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REFERENCES 75 5. DISCUSSION The ana
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INTEGRABILITY OF SDYM EQUATIONS FOR
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Integrability of SDYM Equations for
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REFERENCES 87 [18] [19] [20] [21] [
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II ALTERNATIVE THEORIES AND SCALAR
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THE FRW UNIVERSES WITH BAROTROPIC F
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The FRW Universes with Barotropic F
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REFERENCES 99 (1979) 515; H. Dehnen
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HIGGS-FIELD AND GRAVITY Heinz Dehne
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Higgs-Field and Gravity 103 is defi
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Higgs-Field and Gravity 105 Consequ
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Higgs-Field and Gravity 107 From th
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REFERENCES 109 Evidently by inserti
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THE ROAD TO GRAVITATIONAL S-DUALITY
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The road to Gravitational S-duality
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REFERENCES 121 The partition functi
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EXACT SOLUTIONS IN MULTIDIMENSIONAL
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Exact solutions in multidimensional
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REFERENCES 131 For possible physica
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EFFECTIVE FOUR-DIMENSIONAL DILATON
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Dilaton gravity from Chern-Simons g
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A PLANE-FRONTED WAVE SOLUTION IN ME
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A plane-fronted wave solution in me
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REFERENCES 6. SUMMARY 151 We invest
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III COSMOLOGY AND INFLATION
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NEW SOLUTIONS OF BIANCHI MODELS IN
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New solutions of Bianchi models in
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REFERENCES 163 Further solutions of
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SCALAR FIELD DARK MATTER Tonatiuh M
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Scalar field dark matter 167 tional
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Scalar field dark matter 169 being
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Scalar field dark matter 171 of dar
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Scalar field dark matter 173 growin
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Scalar field dark matter 175 This s
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Scalar field dark matter 177 rotati
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Scalar field dark matter 179 where
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Scalar field dark matter 181 while
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REFERENCES 183 The hypothesis of th
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INFLATION WITH A BLUE EIGENVALUE SP
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Inflation with a blue eigenvalue sp
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REFERENCES 193 problem” for nonli
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CLASSICAL AND QUANTUM COSMOLOGY WIT
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Quantum cosmology with self-interac
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REFERENCES 203 [13] has considered
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THE BIG BANG IN GOWDY COSMOLOGICAL
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Page 238 and 239: THE INFLUENCE OF SCALAR FIELDS IN P
Page 240 and 241: The influence of scalar fields in p
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Page 244 and 245: EXACT SOLUTIONS AND SCALAR FIELDS I
Page 246 and 247: REFERENCES 221 [3] by R.C. Kennicut
Page 248 and 249: ADAPTIVE CALCULATION OF A COLLAPSIN
Page 250 and 251: Adaptive Calculation of a Collapsin
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Page 260 and 261: REVISITING THE CALCULATION OF INFLA
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Page 272 and 273: CONFORMAL SYMMETRY AND DEFLATIONARY
Page 274 and 275: Conformal symmetry and deflationary
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Page 286 and 287: IV EXPERIMENTS AND OTHER TOPICS
Page 288 and 289: STATICITY THEOREM FOR NON-ROTATING
Page 290 and 291: Staticity Theorem for Non-Rotating
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Page 296 and 297: QUANTUM NONDEMOLITION MEASUREMENTS
Page 298 and 299: Quantum nondemolition measurements
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Page 306 and 307: ON ELECTROMAGNETIC THIRRING PROBLEM
Page 308 and 309: On Electromagnetic Thirring Problem
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Page 320 and 321: ON THE EXPERIMENTAL FOUNDATION OF M
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On the experimental foundation of M
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REFERENCES 309 [12] [13] [14] [15]
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LORENTZ FORCE FREE CHARGED FLUIDS I
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Lorentz force free charged fluids i
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REFERENCES 319 force can be foresee
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Index Axisymmetries and configurati
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INDEX 323 Theorem (cont.) staticity
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Prof. Heinz Dehnen: Brief Biography
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Prof. Dietrich Kramer: Brief Biogra
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