Intro; Supervisors' Foreword; Abstract; Acknowledgements; Contents; Abbreviations; Part I Asymptotically Safe Quantum Gravity; 1 Introduction; References; 2 The Wilsonian Idea of Renormalization; 2.1 Scale Invariance, Universality and Kadanoff Blocking Transformations; 2.1.1 The Role of Scaling Laws; 2.1.2 Kadanoff Blocking Transformations; 2.2 The Wilsonian Idea of Renormalization; 2.3 Functional Renormalization Group; 2.3.1 Wilsonian Average Action; 2.3.2 Wegner-Houghton Equation; 2.4 Fixed Points and Generalized Renormalizability; References

3 Functional Renormalization and Asymptotically Safe Gravity3.1 The Wetterich Equation for Scalars; 3.2 The Wetterich Equation for Gauge Theories; 3.2.1 Gauge Fixing and Ghosts; 3.2.2 Background Field Method; 3.2.3 Cutoff Function and Heat-Kernel Techniques; 3.3 Asymptotic Safety in Quantum Einstein Gravity; References; Part II Asymptotically Safe Gravity on Foliated Spacetimes; 4 Quantum Gravity on Foliated Spacetimes; 4.1 Spacetime Foliation and Functional Renormalization; 4.1.1 Arnowitt-Deser-Misner Decomposition of Spacetime; 4.1.2 Renormalization Group Equations on Foliated Spacetimes

4.2 Renormalization Group Flow on a FRW Background4.2.1 The Einstein-Hilbert Ansatz; 4.2.2 Operator Traces on FRW Backgrounds; 4.2.3 Hessians, Gauge-Fixing and Ghost Action; 4.2.4 Regulator and Beta Functions; 4.3 Properties of the Renormalization Group Flow; 4.3.1 Pure Gravity; 4.3.2 Gravity-Matter Systems; 4.4 Universality Classes for Quantum Gravity; 4.4.1 Fixed Points and Universality Classes; 4.4.2 Phase Diagrams; References; Part III Astrophysical and Cosmological Implications of Asymptotic Safety; 5 Inflationary Cosmology from Quantum Gravity-Matter Systems

5.1 CMB Radiation and Cosmic Inflation5.1.1 Cosmic Inflation and Slow-Roll Approximation; 5.2 Asymptotically Safe Inflation from (R+R2)-Gravity; 5.2.1 Motivation and Strategy; 5.2.2 Effective Inflationary Potential from Quadratic Gravity; 5.2.3 Inflaton Dynamics and Primordial Power Spectrum; 5.2.4 Post-inflationary Dynamics; 5.3 Constraints on Early Universe Matter Fields from Foliated Quantum Gravity-Matter Systems; References; 6 Quantum Black Holes and Spacetime Singularities; 6.1 Vaidya-Kuroda-Papapetrou Spacetimes; 6.2 Singularity Structure in Generalized Vaidya Spacetimes

6.3 RG-improved VKP Spacetimes6.3.1 Gravitational Collapse in the RG-improved VKP Spacetime; 6.3.2 Singularity Structure in the RG-improved VKP Spacetime; References; Part IV Conclusions; 7 Conclusions; References; A FRG Equations on Foliated Spacetimes; A.1 Hessians in a FRW Background; A.1.1 Hessians in the Gravitational Sector; A.1.2 Gauge-Fixing Terms; A.2 Evaluation of the Operator Traces; A.2.1 Cutoff Scheme and Master Traces; A.2.2 Trace Contributions in the Gravitational Sector; A.2.3 Minimally Coupled Matter Fields; Appendix Curriculum Vitae et Studiorum