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NEW SOLUTIONS OF BIANCHI MODELS IN SCALAR-TENSOR THEORIES Jorge L. Cervantes–Cota*, M. A. Rodriguez–Meza † , Marcos Nahmad Departamento de Física, Instituto Nacional de Investigaciones Nucleares (ININ) P.O. Box 18–1027, México D.F. 11801, México. Abstract We use scaled variables to display a set coupled equations valid for isotropic and anisotropic Bianchi type I, V, IX models in scalar-tensor theories, including Dehnen’s induced gravity theory. In particular, for the Brans–Dicke theory the equations decouple and one is able to integrate the system for FRW and Bianchi I and V models. Additionally, we analyze the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. Keywords: Scalar–tensor theories, exact solutions, cosmology. 1. INTRODUCTION The CMBR measured by the COBE satellite [1], as well as current cosmological x–ray surveys, imply that the universe is nowadays at big scales homogeneous and isotropic, and must also has been having these properties since, at least, the era of nucleosynthesis [2]. In order to explain the isotropy of the universe from theoretical anisotropic models, many authors have considered the Bianchi models that can in principle evolve to a Friedmann–Robertson–Walker (FRW) cosmology. It has been shown that some Bianchi models in General Relativity (GR) tend to their isotropic solutions, up some extent [3, 4], and even that they can explain the level of anisotropy measured by COBE [5]. Motived by these facts, we have been working in Brans-Dicke (BD) theory [6] to investigate if Bianchi universes are able to isotropize as the universe evolves, and if its evolution can be inflationary. In previous investigations we have shown that anisotropic, Bianchi type I, V, and IX models * E–mail:jorge@nuclear.inin.mx † On leave from Instituto de Física, Universidad Autónoma de Puebla. Exact Solutions and Scalar Fields in Gravity: Recent Developments Edited by Macias et al., Kluwer Academic/Plenum Publishers, New York, 2001 155
156 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY tend to isotropize as models evolve [7, 8]. However, this may happen for some restrictive values of in the cases of Bianchi type I and IX, and only Bianchi type V model can accomplish an isotropization mechanism within BD current constraints [9] on It has been also shown that the isotropization mechanism in the Bianchi type V model can be inflationary, without the presence of any cosmological constant, when small values for the coupling constant are considered [9], as in the case of some induced gravity (IG) models [10, 11]. We have recently shown, however, that the isotropization mechanism can be attained with sufficient amount of e–folds of inflation, only for negative values of [12]. In the present report we present the set of differential equations that have be solve to find solutions of scalar-tensor theories, and particular results are presented for BD theory. This paper is organized as follows. In section 2 FRW and anisotropic equations in scalar–tensor theories are presented in convenient variables. In section 3 we specialize our formalism to the BD theory and review the main results on these cosmological models. Finally, conclusions are in section 4. 2. EQUATIONS FOR FRW AND BIANCHI MODELS In previous investigations [7, 9, 12, 13] we have used scaled variables, in terms of which our solutions have been given, therefore following we use them: the scaled field a new cosmic time parameter the ‘volume’ and the Hubble parameters corresponding to the scale factors for We assume comoving coordinates and a perfect fluid with barotropic equation of state, where is a constant. Using these definitions one obtains the cosmological equations for Bianchi type I, V and IX models (in units with and
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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
Page 130 and 131: Higgs-Field and Gravity 105 Consequ
Page 132 and 133: Higgs-Field and Gravity 107 From th
Page 134 and 135: REFERENCES 109 Evidently by inserti
Page 136 and 137: THE ROAD TO GRAVITATIONAL S-DUALITY
Page 138 and 139: The road to Gravitational S-duality
Page 146 and 147: REFERENCES 121 The partition functi
Page 148 and 149: EXACT SOLUTIONS IN MULTIDIMENSIONAL
Page 150 and 151: Exact solutions in multidimensional
Page 156 and 157: REFERENCES 131 For possible physica
Page 158 and 159: EFFECTIVE FOUR-DIMENSIONAL DILATON
Page 160 and 161: Dilaton gravity from Chern-Simons g
Page 166 and 167: A PLANE-FRONTED WAVE SOLUTION IN ME
Page 168 and 169: A plane-fronted wave solution in me
Page 176 and 177: REFERENCES 6. SUMMARY 151 We invest
Page 178 and 179: III COSMOLOGY AND INFLATION
Page 182 and 183: New solutions of Bianchi models in
Page 188 and 189: REFERENCES 163 Further solutions of
Page 190 and 191: SCALAR FIELD DARK MATTER Tonatiuh M
Page 192 and 193: Scalar field dark matter 167 tional
Page 194 and 195: Scalar field dark matter 169 being
Page 196 and 197: Scalar field dark matter 171 of dar
Page 198 and 199: Scalar field dark matter 173 growin
Page 200 and 201: Scalar field dark matter 175 This s
Page 202 and 203: Scalar field dark matter 177 rotati
Page 204 and 205: Scalar field dark matter 179 where
Page 206 and 207: Scalar field dark matter 181 while
Page 208 and 209: REFERENCES 183 The hypothesis of th
Page 210 and 211: INFLATION WITH A BLUE EIGENVALUE SP
Page 212 and 213: Inflation with a blue eigenvalue sp
Page 218 and 219: REFERENCES 193 problem” for nonli
Page 220 and 221: CLASSICAL AND QUANTUM COSMOLOGY WIT
Page 222 and 223: Quantum cosmology with self-interac
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THE BIG BANG IN GOWDY COSMOLOGICAL
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The Big Bang in Gowdy Cosmological
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THE INFLUENCE OF SCALAR FIELDS IN P
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The influence of scalar fields in p
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The influence of scalar fields in p
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REFERENCES 221 [3] by R.C. Kennicut
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ADAPTIVE CALCULATION OF A COLLAPSIN
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Adaptive Calculation of a Collapsin
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REFERENCES 233 [5] [6] [7] [8] [9]
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REVISITING THE CALCULATION OF INFLA
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Revisiting the calculation of infla
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CONFORMAL SYMMETRY AND DEFLATIONARY
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Conformal symmetry and deflationary
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REFERENCES 259 [16] R. Maartens, D.
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IV EXPERIMENTS AND OTHER TOPICS
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STATICITY THEOREM FOR NON-ROTATING
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Staticity Theorem for Non-Rotating
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Staticity Theorem for Non-Rotating
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REFERENCES 269 The boundary is cons
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QUANTUM NONDEMOLITION MEASUREMENTS
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Quantum nondemolition measurements
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REFERENCES 279 [11] M. Kasevich and
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ON ELECTROMAGNETIC THIRRING PROBLEM
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On Electromagnetic Thirring Problem
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REFERENCES 293 [8] [9] D. Brill and
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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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