## An Introduction to Mathematical CosmologyThis book provides a concise introduction to the mathematical aspects of the origin, structure and evolution of the universe. The book begins with a brief overview of observational and theoretical cosmology, along with a short introduction of general relativity. It then goes on to discuss Friedmann models, the Hubble constant and deceleration parameter, singularities, the early universe, inflation, quantum cosmology and the distant future of the universe. This new edition contains a rigorous derivation of the Robertson-Walker metric. It also discusses the limits to the parameter space through various theoretical and observational constraints, and presents a new inflationary solution for a sixth degree potential. This book is suitable as a textbook for advanced undergraduates and beginning graduate students. It will also be of interest to cosmologists, astrophysicists, applied mathematicians and mathematical physicists. |

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### Contents

III | 1 |

IV | 12 |

V | 18 |

VI | 21 |

VII | 24 |

VIII | 28 |

IX | 32 |

X | 37 |

XL | 122 |

XLI | 126 |

XLII | 128 |

XLIII | 135 |

XLIV | 142 |

XLV | 143 |

XLVI | 148 |

XLVII | 153 |

XI | 42 |

XII | 45 |

XIII | 51 |

XIV | 53 |

XV | 60 |

XVI | 64 |

XVII | 67 |

XVIII | 68 |

XX | 71 |

XXI | 73 |

XXII | 76 |

XXIV | 77 |

XXV | 80 |

XXVI | 85 |

XXVII | 90 |

XXVIII | 94 |

XXIX | 98 |

XXX | 100 |

XXXI | 102 |

XXXII | 104 |

XXXIII | 107 |

XXXIV | 112 |

XXXV | 113 |

XXXVI | 115 |

XXXVII | 118 |

XXXVIII | 120 |

XXXIX | 121 |

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### Common terms and phrases

approximately baryon behaviour big bang black hole chapter clusters consider coordinate corresponding cosmic background radiation cosmological constant covariant critical density curvature curve deceleration parameter defined denoted derivatives deuterium diagram distance early universe Einstein Einstein's equations electrons energy density example expansion finite following equation Friedmann models galaxies geodesic give given as follows gravitational helium Higgs field Hubble Hubble's Hubble's constant Hubble's law hypersurface inflation inflationary models interactions Islam isotropic Killing vectors Lagrangian Lett Lond luminosity mass-energy density matter mentioned earlier Narlikar negative neutrinos neutron nuclei nucleons nucleosynthesis number density observed particles path integral phase transition photons Phvs Phys potential present quantum cosmology quarks quasars ratio red-shift relation right hand side Robertson-Walker metric Sandage scalar field singularity space space-time spatial standard model stars symmetry temperature tends to infinity theory tion transformation vanishes velocity wave function worldline written as follows zero pressure