Regular and chaotic dynamics in scalar field cosmology

Acknowledgments......Page 1
Introduction......Page 11
Scalar fields in cosmology......Page 16
Brans–Dicke theory......Page 17
Kaluza–Klein theory......Page 19
The dilaton from string theory......Page 20
Non-minimal coupling......Page 21
Geometry of chaos in scalar field FRW models......Page 26
FRW models with scalar fields as a simple indefinite dynamical systems......Page 28
Poincaré sections......Page 31
Symbolic dynamics in detection of dynamical complexity......Page 33
Distribution of intersection points on the boundary set......Page 37
Unstable periodic orbits as an indicator of complexity of dynamics......Page 38
Conclusions......Page 40
Scattering processes in cosmological dynamics......Page 45
Hamiltonian dynamics of phantom cosmology......Page 47
Conformally coupled phantom fields......Page 49
The positive quadratic potential function......Page 53
The negative quadratic potential function......Page 54
Phantom cosmology as a scattering process......Page 61
Acceleration in Phantom Cosmology......Page 63
Conclusions......Page 66
Non-minimally coupled scalar field cosmology on the phase plane......Page 73
Non-minimally coupled scalar field cosmologies as a dynamical system......Page 74
Phase space analysis of dynamics......Page 86
Conclusions......Page 93
Twister quintessence scenario......Page 95
Toward a unified description of cosmological evolution......Page 107
The model......Page 108
Dynamics of universe with a potential......Page 113
Finite scale factor initial singularity......Page 114
Inflation with the non-minimal coupling and arbitrary potential......Page 117
Radiation domination epoch generated by non-minimal coupling......Page 123
Matter domination......Page 129
The present accelerated expansion epoch......Page 131
Conclusions......Page 134
Summary and Conclusions......Page 139
Einstein equations and energy–momentum tensor......Page 143
Conformal invariance......Page 148
The Center Manifold Theorem......Page 152
Bibliography......Page 155