Despite the success of general relativity in explaining classical gravitational phenomena, several problems at the interface between gravitation and high energy physics still remain open. The purpose of this thesis is to explore quantum gravity and its phenomenological consequences for dark matter, gravitational waves and inflation. A new formalism to classify gravitational theories based on their degrees of freedom is introduced and, in light of this classification, it is argued that dark matter is no different from modified gravity. Gravitational waves are shown to be damped due to quantum degrees of freedom. The consequences for gravitational wave events are also discussed. The non-minimal coupling of the Higgs boson to gravity is studied in connection with Starobinsky inflation and its implications for the vacuum instability problem is analyzed.

Gravity beyond general relativity / Kazuya Koyama -- Parametrizations for tests of gravity / Lucas Lombriser -- Simulation techniques / Claudio Llinares -- Approximation methods in modified gravity models / Baojiu Li -- Large-scale structure probes of modified gravity / Catherine Heymans and Gong-Bo Zhao -- Tests of gravity with galaxy clusters / Matteo Cataneo -- Towards testing gravity with cosmic voids / Yan-Chuan Cai -- Astrophysical tests of screened modified gravity / Jeremy Sakstein -- Laboratory constraints / Philippe Brax.

Beyond 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.

Beyond 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.

Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.

This work investigates the theoretical and cosmological implications of modifying Einstein's theory of general relativity. It explores two classes of modifications to gravity: those in which the graviton is given a small mass, and those in which Lorentz invariance is spontaneously broken. It elucidates the nature of cosmological perturbations in theories of massive bimetric gravity, including a potentially deadly instability. Theories of gravity beyond general relativity could explain why the expansion of the Universe is accelerating, obviating the need for a dark energy, and can also affect the evolution of the early Universe. Next, it investigates the nature of spacetime in massive gravity theories that contain two different spacetime metrics. Lastly, the strongest constraints to date are placed on the size of Lorentz-violating effects in the gravity sector during inflation.