University of Crete Department of Physics Cosmological evolution in brane-worlds 6 0 with large transverse dimensions: 0 2 Inflation and dark matter y a M 2 A Doctoral Dissertation 2 v 2 5 1 G. Panotopoulos 4 0 6 0 / h p - p e h : v i X r a Heraklion, Greece, April 2006 Grigoris Panotopoulos Cosmological evolution in brane-worlds with large transverse dimensions: Inflation and dark matter A Dissertation submitted to the Department of Physics, University of Crete in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Physics Heraklion, Greece, April 2006 Cosmological evolution in brane-worlds with large transverse dimensions: Inflation and dark matter Thesis author Grigoris Panotopoulos Thesis supervisor Prof. T. N. Tomaras Thesis committee T. N. Tomaras E. Kiritsis I. Antoniadis N. Tsamis A. Petkou P. Ditsas N. Papanicolaou N. D. Kylafis Department of Physics, University of Crete Heraklion, Greece 2006 Contents Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . vi Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1 Introduction 1 1.1 Gauge Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Fermion Problem . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Higgs/hierarchy Problem . . . . . . . . . . . . . . . . . . . . . 2 1.4 Strong CP Problem . . . . . . . . . . . . . . . . . . . . . . . . 3 1.5 Graviton Problem . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.6 Dark sector problem . . . . . . . . . . . . . . . . . . . . . . . 4 1.7 The brane-world idea . . . . . . . . . . . . . . . . . . . . . . . 5 PART I: The Theoretical Framework 7 2 The brane-world scenario 8 2.1 Randall-Sundrum localization . . . . . . . . . . . . . . . . . . 8 2.2 Brane-Induced gravity . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Randall-Sundrum plus brane–induced gravity . . . . . . . . . 12 3 Preliminaries 13 3.1 The Standard Model of particle physics and supersymmetry . 13 3.1.1 The SM of particle physics . . . . . . . . . . . . . . . . 13 3.1.2 Basics of Supersymmetry . . . . . . . . . . . . . . . . . 20 3.2 The Standard Model of Cosmology, the early Universe and inflation 26 3.2.1 The SM of cosmology . . . . . . . . . . . . . . . . . . . 26 i 3.2.2 The early Universe . . . . . . . . . . . . . . . . . . . . 34 3.2.3 Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . 46 PART II: Cosmological evolution, inflation and dark matter in brane cosmology 57 4 Axino dark matter 58 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5 Sneutrino inflation 67 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.2 Sneutrino inflation in a GB brane-world . . . . . . . . . . . . 69 5.2.1 GB brane-world . . . . . . . . . . . . . . . . . . . . . . 69 5.2.2 Chaotic inflation in a GB brane-world . . . . . . . . . 71 5.3 Reheating, gravitino production and leptogenesis . . . . . . . 74 5.3.1 Reheating . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.3.2 Gravitino production . . . . . . . . . . . . . . . . . . . 75 5.3.3 Direct leptogenesis from sneutrino decay . . . . . . . . 77 5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6 D-term inflation 82 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.2 D-term inflation . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.3 Effective gravitational equations on the brane . . . . . . . . . 85 6.4 Inflationary dynamics on the brane . . . . . . . . . . . . . . . 86 6.5 Reheating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 7 Brane-Bulk energy exchange 93 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 7.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 7.3 Critical point analysis . . . . . . . . . . . . . . . . . . . . . . 101 7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 ii 8 Conclusions 107 iii List of Figures 6.1 Reheating temperature T versus the superpotential coupling λ for M = 1010 GeV and R 1 6.2 Reheating temperature T versus the Fayet-Iliopoulos term ξ for superpotential coupling R 7.1 Influx, w = 0, ν < 3/2. The arrows show the direction of increasing cosmic time. The dotted 7.2 Outflow, w = 1/3, ν < 3/2. The arrows show the direction of increasing cosmic time. The iv