Models of Disformally Coupled Dark Energy

Acknowledgments......Page 3
Resumo......Page 5
Abstract......Page 9
List of Tables......Page 15
List of Figures......Page 17
1.1 Dynamical Systems......Page 19
1.1.1 Linear Stability Theory......Page 22
1.1.2 Bifurcations......Page 23
1.2 Basics of General Relativity......Page 27
1.3 Standard Model of Cosmology - The FLRW model......Page 30
1.4 Dark Energy......Page 34
1.4.1 Quintessence Field and Tachyon Field......Page 36
2 Conformal and Disformal Transformations......Page 39
2.1 Lagrangian Formalism of GR......Page 40
2.2 Conformal Transformations......Page 43
2.3 Disformal Transformations......Page 45
2.4 Einstein Frame and Jordan Frame......Page 48
2.5 Interacting Dark Energy......Page 50
3.1 The Model......Page 53
3.2 Background Cosmology......Page 56
3.3 Dynamical Equations......Page 58
3.4 Phase Space and Invariant Sets......Page 61
3.5.1 Fixed Points, Stability and Phenomenology......Page 62
3.5.3 Physical Phase Diagram......Page 67
3.6 Viable Cosmologies......Page 70
3.7 Effective Potential......Page 72
3.8 Summary......Page 75
4.1 The Model......Page 77
4.2 Background Cosmology......Page 80
4.3 Dynamical Equations......Page 82
4.4 Phase Space and Invariant Sets......Page 85
4.5.1 Fixed points, Stability and Phenomenology for a pressureless fluid......Page 86
4.5.2 Fixed points, Stability and Phenomenology for a relativistic fluid......Page 91
4.6 Conclusions......Page 94
5 Final Remarks......Page 97
Bibliography......Page 99
A Natural Units......Page 115
B Conformally Coupled Tachyonic Dark Energy - Linear Stability Matrix......Page 118
C Conformally Coupled Tachyonic Dark Energy - Eigenvalues of the Stability Matrix......Page 119
D Disformally Coupled Quintessence - Equation of Motion......Page 121
E Disformally Coupled Quintessence - Interaction term......Page 123
F Fixed Points for the Disformally Coupled System with no Kinetic Dependence......Page 125
G Disformally Coupled Quintessence - Eigenvalues of the Stability Matrix......Page 127