Modified Gravity and Cosmology

Introduction.- General Relativity.- Foundations of gravity - modifications and extensions.- Part I: Theories of Gravity.- Introduction.- A avour on f(R) theories: theory and observations.- Horndeski/Galileon theories.- Massive Gravity and Bimetric Gravity.- Gravity in extra dimensions.- Non-local models.- Metric-A ne gravity.- Geometric Foundations of Gravity.- Palatini theories of gravity.- Hybrid metric-Palatini gravity and cosmology.- Teleparallel and f(T) Gravity: Foundations and Cosmology.- Finsler gravity .- Gravity's Rainbow.- Quantum Cosmology in modified theories of gravity.- Part II: Testing Relativistic E ects.- Introduction.- Laboratory Constraints .- Screening mechanisms.- Microscopic e ects of modified gravity.- Compact stars as tests of modified gravity.- Compact objects in General Relativity and beyond.- Parametrized post-Newtonian formalism.- Gravitational Waves .- Gravitational lensing.- Classicalizing gravity.- Part III: Cosmology and Observational Discriminators.- Introduction.- Phenomenological tests of gravity on cosmological scales.- Relativistic e ects.- Cosmological constraints from the e ective field theory of dark energy .- The H0 tensions to discriminate among concurring models.- s8 tension. Is gravity getting weaker at low z? Observational evidence and theoretical implications.- Testing gravity with standard sirens: challenges and opportunities.- Testing the dark universe with cosmic shear.- Galaxy clusters and modified gravity.- Probing screening modified gravity with non-linear structure formation .- Conclusions.- Outlook.- The end of the beginning.

Emmanuel N. Saridakis obtained his BSc in Physics from the University of Athens, his MSc from Imperial College/UK, while he obtained his PhD in Cosmology from the Physics Department of the University of Athens. He has worked as a Postdoctoral Researcher at the Physics Department of the University of Athens, at the Institut de Physique Théorique Saclay/France, at the National Tsing Hua University/Taiwan, and at the Physics Department of the National Technical University of Athens. He has worked as visiting Professor at the Institut d'Astrophysique de Paris/France, at the Pontificia Universidad Catolica Valparaiso/Chile, and as an Assistant Professor 407 at the Physics Department of the National Technical University of Athens. He is an Adjunct Professor at the Physics Department of Baylor University/USA, and Professor at the Astronomy Department of the University of Science and Technology/China. He is Principal Researcher in the National Observatory of Athens. His interests are cosmology, relativity, theories of gravity, dark energy, dark matter, inflation, astrophysical and cosmological implications of modified theories of gravity, observational cosmology, cosmological data analysis.
Ruth Lazkoz got her Phd from the University of the Basque Country with a thesis on exact inhomogeneous solutions of the Einstein field equation in cosmology. She was a postdoc for two years at Queen Mary College (London), and then got back to her alma mater in 2001 where she has been doing research and teaching since. Her current interests are observational constraints on dark energy and modified gravity cosmological models, and in parallel she continues to work on dynamical systems studies of that kind of scenarios. She has been the Chairperson of the COST Action CANTATA CA15117 and an associate editor for General Relativity and Gravitation. She is currently the President of the Spanish Society of Gravitation and Relativity.
Vincenzo Salzano received his Ph.D. in Fundamental and