Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

More documents

Recommendations

Info

REFERENCES 193 problem” for nonlinear equations [26]. However, in the case of inflation the bifurcation into regimes of stability or instability depends in the first place on the behavior of the exact autonomous system (2), which has already been analyzed [17, 27] under the more general aspect of catastrophe theory. Moreover, there have been recently raised some reservations [28] on the applicability and consistency of the second order slow–roll approximation, which need to be investigated further. Summarizing, the nonlinear Abel equation (6) permits exact solutions for the discrete or continuous eigenvalues of Table 1. All positive discrete values are marginally consistent with the from COBE as well as recent ground-based CMB experiments like BOOMERANG, our highest value for the blue spectrum is just below the constraint in order to suppress distortions of the microwave spectrum and the formation of primordial black holes during the phase of reheating, cf. Ref. [3]. Since our blue discrete spectrum has the scale invariant Harrison– Zel‘dovich solution as limiting point our expectations are high for the new more accurate constraints [29] the future PLANCK satellite will provide for inflation. Acknowledgments We would like to thank Ed Copeland, Andrew Liddle, Alfredo Macías, and Anupam Mazumdar for useful comments and hints to the literature. This work was partially supported by CONACyT, grant No. 28339–E, the grant P/FOMES 98-35-15, and the joint German–Mexican project DLR–Conacyt E130–1148 and MXI 010/98 OTH. One of us (E.W.M.) would like to thank his wife Noelia Méndez Córdova for encouragement and love. References [1] [2] [3] [4] [5] [6] [7] [8] [9] A.R. Liddle and D.H. Lyth, Phys. Rep. 231 (1993) 1. F.E. Schunck and E.W. Mielke, Phys. Lett. B485 (2000) 231. J.E. Lidsey, A.R. Liddle, E.W. Kolb, E.J. Copeland, T. Barriero, and M. Abney, Rev. Mod. Phys. 69 (1997) 373. E.J. Copeland, E.W. Kolb, A.R. Liddle and J.E. Lidsey, Phys. Rev. D49 (1994) 1840. F.E. Schunck and E.W. Mielke, Phys. Rev. D50 (1994) 4794. E.W. Mielke and F.E. Schunck, Phys. Rev. D52 (1995) 672. A.R. Liddle, A. Mazumdar, and F.E. Schunck, Phys. Rev. D58 (1998) R061301. C.L. Bennett et al., Astrophys. J. 436 (1994) 423; Astrophys. J. Lett. 464 (1996) L1. P.F. Scott et al., Astrophys. J. Lett. 461 (1996) L1.
194 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY [10] P. de Bernadis et al., Nature (London) 404 (2000) 955. [11] A.N. Lasenby, A.W. Jones, and Y. Dabrowski: Review of ground-based CMB experiments, in: Proc. Moriond Workshop, Les Arcs; France 1998, astro-ph/9810175. [12] S. Dodelson and L. Knox, Phys. Rev. Lett. 84 (2000) 3523; L. Knox and L. Page, Phys. Rev. Lett. 85 (2000) 1366. [13] E.D. Stewart and D.H. Lyth, Phys. Lett. B302 (1993) 171. [14] D.H. Lyth and E.D. Stewart, Phys. Lett. B274 (1992) 168. [15] I.J. Grivell and A.R. Liddle, Phys. Rev. D54 (1996) 7191. [16] E.W. Mielke, O. Obregón and A. Macías, Phys. Lett. B391 (1997) 281. [17] F.V. Kusmartsev, E.W. Mielke, Yu.N. Obukhov and F.E. Schunck, Phys. Rev. D51 (1995) 924. [18] E.W. Mielke, in: Proc. of the Eighteenth Texas Symposium on Relativistic Astrophysics and Cosmology, “Texas in Chicago”, 15–20 Dec. 1996, eds. A.V. Olinto, J.A. Frieman, and D.N. Schramm (World Scientific, Singapore, 1998), pp. 688. [19] J. Devlin, N.G. Lloyd and J.M. Pearson, J. Diff. Eq. 147 (1998) 435 . [20] A. García, A. Macías and E.W. Mielke, Phys. Lett. A229 (1997) 32. [21] J. Benítez, A. Macías, E.W. Mielke, O. Obregón, and V.M. Villanueva, Int. J. Mod. Phys. A12 (1997) 2835. [22] F.E. Schunck, Ann. Phys. (Leipzig) 2 (1993) 647. [23] R. Easther, Class. Quantum Grav. 13 (1996) 1775. [24] E.W. Kolb: Inflation in the postmodern era, Proceedings of the Erice School, Astrofundamental Physics, astro-ph/9612138. [25] A.D. Linde, Phys. Rev. D49 (1994) 748; E.J. Copeland, A.R. Liddle, D.H. Lyth, E.D. Stewart, and D. Wands, Phys. Rev. D49 (1994) 6410. [26] E. Ayón-Beato, A. García, R. Mansilla, and C.A. Terrero-Escalante, Phys. Rev. D62 (2000) 103513. [27] A. García, A. Macías, and E.W. Mielke (1998): Extended inflation and catastrophe theory, in: Recent Developments in Gravitation and Mathematical Physics, Proc. of the 2nd Mexican School on Gravitation and Mathematical Physics, eds. A. García, C. Lämmerzahl, A. Macías, T. Matos, and D. Nunez, ISBN 3–9805735– 0–8 (Science Network Publ., Konstanz, 1996). [28] J. Martin and D. Schwarz, Phys. Rev. D62 (2000) 103520. [29] A.R. Liddle, Contemp. Phys. 39 (1998) 95.
Page 2 and 3:
EXACT SOLUTIONS AND SCALAR FIELDS I
Page 4 and 5:
EXACT SOLUTIONS AND SCALAR FIELDS I
Page 6 and 7:
To the 65th birthday of Heinz Dehne
Page 8 and 9:
CONTENTS Preface Contributing Autho
Page 10 and 11:
Contents ix 5 The case of 84 Part I
Page 12 and 13:
Contents xi Luis O. Pimentel, Cesar
Page 14 and 15:
Contents xiii 2.2 String theory ind
Page 16 and 17:
PREFACE This book is dedicated to h
Page 18 and 19:
CONTRIBUTING AUTHORS Eloy Ayón-Bea
Page 20 and 21:
Contributing Authors xix Jaime Klap
Page 22 and 23:
Contributing Authors xxi A.P. 70-54
Page 24 and 25:
Contributing Authors xxiii L. Artur
Page 26 and 27:
I EXACT SOLUTIONS
Page 28 and 29:
SELF-GRAVITATING STATIONARY AXI- SY
Page 30 and 31:
Self-gravitating stationary axisymm
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
REFERENCES 13 be shown that the ana
Page 40 and 41:
NEW DIRECTIONS FOR THE NEW MILLENNI
Page 42 and 43:
New Directions for the New Millenni
Page 44 and 45:
New Directions for the New Millenni
Page 46 and 47:
REFERENCES 21 Acknowledgments The r
Page 48 and 49:
ON MAXIMALLY SYMMETRIC AND TOTALLY
Page 50 and 51:
On maximally symmetric and totally
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
DISCUSSION OF THE THETA FORMULA FOR
Page 66 and 67:
Theta formula for the Ernst potenti
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
REFERENCES 51 Rosenhain’s theta f
Page 78 and 79:
THE SUPERPOSITION OF NULL DUST BEAM
Page 80 and 81:
The superposition of null dustbeams
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
REFERENCES 61 geodesic with respect
Page 88 and 89:
SOLVING EQUILIBRIUM PROBLEM FOR THE
Page 90 and 91:
Solving equilibrium problem for the
Page 92 and 93:
REFERENCES 67 where the subindices
Page 94 and 95:
ROTATING EQUILIBRIUM CONFIGURATIONS
Page 96 and 97:
Rotating equilibrium configurations
Page 98 and 99:
Rotating equilibrium configurations
Page 100 and 101:
REFERENCES 75 5. DISCUSSION The ana
Page 102 and 103:
INTEGRABILITY OF SDYM EQUATIONS FOR
Page 104 and 105:
Integrability of SDYM Equations for
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
REFERENCES 87 [18] [19] [20] [21] [
Page 114 and 115:
II ALTERNATIVE THEORIES AND SCALAR
Page 116 and 117:
THE FRW UNIVERSES WITH BAROTROPIC F
Page 118 and 119:
The FRW Universes with Barotropic F
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
REFERENCES 99 (1979) 515; H. Dehnen
Page 126 and 127:
HIGGS-FIELD AND GRAVITY Heinz Dehne
Page 128 and 129:
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 140 and 141:
Page 142 and 143:
Page 144 and 145:
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 152 and 153:
Page 154 and 155:
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 162 and 163:
Page 164 and 165:
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 180 and 181: NEW SOLUTIONS OF BIANCHI MODELS IN
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 220 and 221: CLASSICAL AND QUANTUM COSMOLOGY WIT
Page 222 and 223: Quantum cosmology with self-interac
Page 228 and 229: REFERENCES 203 [13] has considered
Page 230 and 231: THE BIG BANG IN GOWDY COSMOLOGICAL
Page 232 and 233: The Big Bang in Gowdy Cosmological
Page 238 and 239: THE INFLUENCE OF SCALAR FIELDS IN P
Page 240 and 241: The influence of scalar fields in p
Page 242 and 243: The influence of scalar fields in p
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
Page 258 and 259: REFERENCES 233 [5] [6] [7] [8] [9]
Page 260 and 261: REVISITING THE CALCULATION OF INFLA
Page 262 and 263: Revisiting the calculation of infla
Page 268 and 269:
Revisiting the calculation of infla
Page 270 and 271:
Revisiting the calculation of infla
Page 272 and 273:
CONFORMAL SYMMETRY AND DEFLATIONARY
Page 274 and 275:
Conformal symmetry and deflationary
Page 276 and 277:
Page 278 and 279:
Page 280 and 281:
Page 282 and 283:
Page 284 and 285:
REFERENCES 259 [16] R. Maartens, D.
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
Page 292 and 293:
Staticity Theorem for Non-Rotating
Page 294 and 295:
REFERENCES 269 The boundary is cons
Page 296 and 297:
QUANTUM NONDEMOLITION MEASUREMENTS
Page 298 and 299:
Quantum nondemolition measurements
Page 300 and 301:
Page 302 and 303:
Page 304 and 305:
REFERENCES 279 [11] M. Kasevich and
Page 306 and 307:
ON ELECTROMAGNETIC THIRRING PROBLEM
Page 308 and 309:
On Electromagnetic Thirring Problem
Page 310 and 311:
Page 312 and 313:
Page 314 and 315:
Page 316 and 317:
Page 318 and 319:
REFERENCES 293 [8] [9] D. Brill and
Page 320 and 321:
ON THE EXPERIMENTAL FOUNDATION OF M
Page 322 and 323:
On the experimental foundation of M
Page 324 and 325:
Page 326 and 327:
Page 328 and 329:
Page 330 and 331:
Page 332 and 333:
Page 334 and 335:
REFERENCES 309 [12] [13] [14] [15]
Page 336 and 337:
LORENTZ FORCE FREE CHARGED FLUIDS I
Page 338 and 339:
Lorentz force free charged fluids i
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
REFERENCES 319 force can be foresee
Page 346 and 347:
Index Axisymmetries and configurati
Page 348 and 349:
INDEX 323 Theorem (cont.) staticity
Page 350 and 351:
Prof. Heinz Dehnen: Brief Biography
Page 352 and 353:
Prof. Dietrich Kramer: Brief Biogra
show all

Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

Create successful ePaper yourself

Delete template?

Save as template?