## Beyond Einstein Gravity: A Survey of Gravitational Theories for Cosmology and AstrophysicsBeyond Einstein’s Gravity is a graduate level introduction to extended theories of gravity and cosmology, including variational principles, the weak-field limit, gravitational waves, mathematical tools, exact solutions, as well as cosmological and astrophysical applications. The book provides a critical overview of the research in this area and unifies the existing literature using a consistent notation. Although the results apply in principle to all alternative gravities, a special emphasis is on scalar-tensor and f(R) theories. They were studied by theoretical physicists from early on, and in the 1980s they appeared in attempts to renormalize General Relativity and in models of the early universe. Recently, these theories have seen a new lease of life, in both their metric and metric-affine versions, as models of the present acceleration of the universe without introducing the mysterious and exotic dark energy. The dark matter problem can also be addressed in extended gravity. These applications are contributing to a deeper understanding of the gravitational interaction from both the theoretical and the experimental point of view. An extensive bibliography guides the reader into more detailed literature on particular topics. |

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### Contents

1 | |

Mathematical tools | 41 |

The landscape beyond Einstein gravity | 59 |

Spherical symmetry | 107 |

Weakfield limit | 165 |

Qualitative analysis and exact solutions in cosmology | 209 |

Cosmology | 261 |

From the early to the present universe | 347 |

Appendix A Physical constants
and astrophysical and cosmological parameters | 391 |

The Noether symmetry approach to fR gravity | 395 |

The weakfield limit of metric fR gravity | 399 |

401 | |

425 | |

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### Common terms and phrases

ˇ ˇ ˇ action approach assume black hole Brans-Dicke theory conformal transformation consider constraint coordinates corresponding cosmographic parameters cosmological constant cosmological models curvature dark energy dark matter degrees of freedom derivatives described discussed dynamics effective Einstein equations Einstein frame energy density equivalent ETGs expansion field equations FLRW universe formalism Friedmann equation function f.R geodesic gravitational coupling gravitational potential gravitational waves higher order Hilbert-Einstein horizon Hubble inflation interaction Jebsen-Birkhoff theorem Jordan frame mass matter fields metric f.R metric g Newtonian Noether symmetry non-minimal coupling observed obtained Palatini f.R particles perturbations phase space physical post-Newtonian principle quantities quantum redshift Ricci scalar satisfy scalar field scalar-tensor gravity scalar-tensor theories scale factor Schwarzschild Sitter SNeIa spacetime spatially flat spherically symmetric solutions static stress-energy tensor theories of gravity tion vacuo vacuum vanishes variables vector weak-field limit yields