# 402-0393-00L Theoretical Cosmology and Different Aspects of Gravity

Semester | Autumn Semester 2020 |

Lecturers | L. Heisenberg |

Periodicity | yearly recurring course |

Course | Does not take place this semester. |

Language of instruction | English |

Abstract | These lecture series will be dedicated to different advanced topics within the framework of theoretical cosmology and gravity. A detailed introduction into the successful construction of General Relativity and beyond will be given, together with their cosmological implications. |

Objective | These lecture series will discuss different advanced topics within the framework of theoretical cosmology and gravity. First of all, I will give a detailed introduction into the successful construction of General Relativity from a geometrical perspective. After constructing our geometrical setup I will discuss the most general space-time geometries and their different manifestations. This will also allow me to introduce the geometrical trinity of gravity, in which the same theory of General Relativity can be constructed a la Einstein based on curvature, a la TEGR based on torsion and a la CGR based on non-metricity, which represents a simpler formulation of General Relativity. Starting from the defining key properties of General Relativity I will explain in which consistent ways these properties can be altered. Still following the geometrical interpretation of gravity this will allow me to introduce modifications of gravity based on affine structure. In the second part I will abandon the geometrical framework and adapt to the field theory perspective. In this context I will construct General Relativity as the unique fundamental theory for a massless spin-2 field. This means that any modification of gravity will ultimately introduce additional degrees of freedom in the gravity sector. After discussing the building blocks of field theories, I will introduce massive gravity, Horndeski scalar-tensor theories, generalized Proca theories and scalar-vector-tensor theories. Based on the assumption that General Relativity is the underlying theory of gravity I will introduce the standard model of cosmology and discuss the tenacious challenges we are facing within this framework. We will study the FLRW models relevant for inflation and late-time universe at the background level and consider small cosmological perturbations together with their evolution. We will see how we can use different observational channels and theoretical consistency checks in order to critically assess different gravity theories. In this context we will pay special attention to the implications of gravitational waves measurements for generalizations of gravity theory beyond General Relativity. Using specialized Mathematica packages some of the relevant relations and computations will be illustrated as well. |

Literature | The lecture follows the review „A systematic approach to generalizations of General Relativity and their cosmological implications“ by L. Heisenberg, Physics Reports 796 (2019) 1-113, arXiv:1807.01725 |