## Dynamical Systems and CosmologyDynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary differential equations. In this book we discuss cosmological models as dynamical systems, with particular emphasis on applications in the early Universe. We point out the important role of self-similar models. We review the asymptotic properties of spatially homogeneous perfect fluid models in general relativity. We then discuss results concerning scalar field models with an exponential potential (both with and without barotropic matter). Finally, we discuss the dynamical properties of cosmological models derived from the string effective action. This book is a valuable source for all graduate students and professional astronomers who are interested in modern developments in cosmology. |

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### Contents

I | ix |

II | xi |

III | ii |

IV | x |

V | 13 |

VI | 14 |

VII | 15 |

VIII | 17 |

LI | 96 |

LII | 97 |

LIII | 98 |

LV | 100 |

LVI | 101 |

LVII | 103 |

LVIII | 104 |

LIX | 106 |

IX | 19 |

X | 21 |

XI | 23 |

XIII | 27 |

XIV | 28 |

XV | 30 |

XVI | 33 |

XVII | 36 |

XVIII | 39 |

XIX | 40 |

XX | 42 |

XXI | 44 |

XXIII | 46 |

XXIV | 48 |

XXV | 50 |

XXVI | 52 |

XXVII | 53 |

XXVIII | 55 |

XXIX | 57 |

XXX | 59 |

XXXII | 60 |

XXXIII | 62 |

XXXIV | 63 |

XXXV | 67 |

XXXVII | 69 |

XXXVIII | 73 |

XXXIX | 76 |

XL | 80 |

XLI | 82 |

XLII | 83 |

XLIII | 84 |

XLIV | 85 |

XLVI | 88 |

XLVIII | 90 |

XLIX | 91 |

L | 94 |

LX | 107 |

LXI | 109 |

LXII | 111 |

LXIII | 112 |

LXIV | 116 |

LXV | 118 |

LXVI | 121 |

LXVIII | 123 |

LXIX | 124 |

LXX | 125 |

LXXI | 129 |

LXXII | 130 |

LXXIII | 132 |

LXXIV | 134 |

LXXV | 135 |

LXXVI | 138 |

LXXVII | 140 |

LXXVIII | 141 |

LXXIX | 142 |

LXXX | 146 |

LXXXI | 148 |

LXXXII | 150 |

LXXXIII | 152 |

LXXXIV | 156 |

LXXXV | 157 |

LXXXVI | 159 |

LXXXVII | 161 |

LXXXVIII | 162 |

LXXXIX | 163 |

XC | 166 |

XCII | 168 |

XCIII | 171 |

XCIV | 174 |

175 | |

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### Common terms and phrases

3-dimensional phase space 3-form potential 4-dimensional anisotropic attractor axion field barotropic Bianchi models Bianchi type central charge deficit compactification cosmological constant cosmological models defined denoted dilaton dilaton field dilaton-vacuum dimensional dimensions discussed dynamical system effective action eigenvalues equilibrium points evolution equations existence exponential potential field strength flat FRW FRW models given Hardbound hence heteroclinic homogeneous models inflation inhomogeneous invariant set ISBN isotropic Kasner late-time attractor Lett line L+ linear M-theory magnetic field massless scalar field matter scaling solution metric modulus field monotonic function non-linear NS-NS parameter perfect fluid periodic orbits perturbations phase space Phys physical power-law inflationary pre-big bang qualitative analysis Quantum Grav recollapse represents scalar field scalar field models scalar-tensor theories self-similar shear singularity sinks spacetime spatial curvature spatially homogeneous models stable string cosmologies string theory studied subset supergravity tensor Theorem two-field type IX models vacuum variables vector Wainwright zero zero-curvature