When predictions of Einstein's theory of General Relativity are compared against observations of our Universe, a huge inconsistency is found. The most popular fix for this inconsistency is to "invent" around 94% of the content of the universe: dark matter and dark energy. The dark energy is some exotic substance responsible for the apparent observed acceleration of the Universe. Another fix is to modify the theory of gravity: it is entirely plausible that Einstein's theory of General Relativity breaks down on cosmological scales, just as Newton's theory of gravity breaks down in the extreme gravitational field of the Sun. There are many alternative theories of gravity, each with the aim of describing observations of our Universe where General Relativity fails. Whether it is dark energy or some modified theory of gravity, it is clear that there is some "dark sector" in the Universe. In this thesis the author constructs a unifying framework for understanding the observational impact of general classes of dark sector theories, by formulating equations of state for the dark sector perturbations.

When recent observational data and the GR+FRW+CDM model are combined we obtain the result that the Universe is accelerating, where the acceleration is due to some not-yet-understood "dark sector". There has been a considerable number of theoretical models constructed in an attempt to provide a description of the dark sector: dark energy and modified gravity theories. The proliferation of modified gravity and dark energy models has brought to light the need to construct a "generic" way to parameterize perturbations in the dark sector. In this thesis we discuss our new way of approaching this problem. We write down an effective action for linearized perturbations to the gravitational field equations for a given field content and use it to compute generalized gravitational field equations for linearized perturbations. Our approach is inspired by that taken in particle physics, where the most general modifications to the standard model are written down for a given field content that is compatible with some assumed symmetry (which we take to be isotropy of the background spatial sections). After applying the formalism we obtain equations of state for dark sector perturbations, where the number of free parameters for wide classes of theories are identified.

Modified gravity theories have been a main focus of theoretical cosmology research in the past decade or so, and have been quickly developing into a mature research field that attracts attention, interest and effort from both theoretical and observational cosmologists. To be prepared for fully exploiting the future observational data, and to provide a guidance for people who are new to this field, it is useful to have a comprehensive review to summarise the current state of knowledge and to foresee the future developments.This book presents expert reviews on different topics in the field, which are then coordinated and organised in a self-consistent and self-contained manner. It is suitable for graduate students and researchers interested in the frontier research of gravity theories.

Introducing the theoretical ideas, observational methods and results in dark energy, this textbook is a thorough introduction to dark energy for graduate courses.

This comprehensive textbook is devoted to classical and quantum cosmology, with particular emphasis on modern approaches to quantum gravity and string theory and on their observational imprint. It covers major challenges in theoretical physics such as the big bang and the cosmological constant problem. An extensive review of standard cosmology, the cosmic microwave background, inflation and dark energy sets the scene for the phenomenological application of all the main quantum-gravity and string-theory models of cosmology. Born of the author's teaching experience and commitment to bridging the gap between cosmologists and theoreticians working beyond the established laws of particle physics and general relativity, this is a unique text where quantum-gravity approaches and string theory are treated on an equal footing. As well as introducing cosmology to undergraduate and graduate students with its pedagogical presentation and the help of 45 solved exercises, this book, which includes an ambitious bibliography of about 3500 items, will serve as a valuable reference for lecturers and researchers.

The modern cosmology has been turned into an outstanding field of active research through the years. Today, we have more scientific data in modern cosmology than we could get rid of it, which makes the present days an exciting era for scientific knowledge. "Trends in Modern Cosmology" invites the reader to tackle the big questions of the universe from cultural aspects of cosmology and its influence on arts, philosophy, and politics to more specialized technical advances in the field as the physics of dark sector, black holes, galaxies, large structure formation, and particles. In fact, it reveals our endless searching for the better understanding of the universe as a legacy of knowledge for next generations.

The Encyclopedia of Cosmology is a new and exciting project which will be a major, long-lasting, seminal reference (a set of four major volumes) at the graduate student level, laid out by the most prominent, respected researchers in the general field of Cosmology. These volumes will be a comprehensive review of the most important concepts and current status in the field of Cosmology of the Universe, covering both theory and observation.One of the most exciting parts of the encyclopedia is that it will exist in both print and, more importantly, electronic forms, perhaps even with some level of interactivity with material such as expanded explanations, movie clips, dynamic pictures, examples of on-line computation, etc. The electronic version will also reflect constant updates of the material. It will be a truly unique publication, unlike anything any of us have seen or known of in existence today.This comprehensive encyclopedia is edited by Dr. Giovanni Fazio from Harvard Smithsonian Center for Astrophysics, with an advisory board comprised of renowned scientists: Lars Hernquist and Abraham Loeb (Harvard Smithsonian Center for Astrophysics), and Christopher McKee (UC Berkeley). Each volume is authored/edited by a specialist in the area: Galaxy Formation and Evolution written by Rennan Barkana (Tel Aviv University), Numerical Simulations in Cosmology edited by Kentaro Nagamine (Osaka University / University of Nevada), Dark Energy written by Shinji Tsujikawa (Tokyo University of Science), and Dark Matter written by Jihn Kim (Seoul National University).

This book contains the proceedings of the International Astronomical Union Symposium no. 225, held in July 2004 at the Ecole Polytechnique Federale de Lausanne (EPFL), in Lausanne, Switzerland. The meeting focused on the applications of gravitational lensing to cosmological physics, and this book summarizes the most recent theoretical and observational developments. With chapters written by leading scientists in the field, this is a valuable resource for professional astronomers and graduate students in astronomy, physics and astro-particle physics.

In the last few years modified gravity theories have been proposed as extensions of Einstein's theory of gravity. Their main motivation is to explain the latest cosmological and astrophysical data on dark energy and dark matter. The study of general relativity at small scales has already produced important results (cf e.g. LNP 863 Quantum Gravity and Quantum Cosmology) while its study at large scales is challenging because recent and upcoming observational results will provide important information on the validity of these modified theories. In this volume, various aspects of modified gravity at large scales will be discussed: high-curvature gravity theories; general scalar-tensor theories; Galileon theories and their cosmological applications; F(R) gravity theories; massive, new massive and topologically massive gravity; Chern-Simons modifications of general relativity (including holographic variants) and higher-spin gravity theories, to name but a few of the most important recent developments. Edited and authored by leading researchers in the field and cast into the form of a multi-author textbook at postgraduate level, this volume will be of benefit to all postgraduate students and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.

This unique thesis covers all aspects of theories of gravity beyond Einstein’s General Relativity, from setting up the equations that describe the evolution of perturbations, to determining the best-fitting parameters using constraints like the microwave background radiation, and ultimately to the later stages of structure formation using state-of-the-art N-body simulations and comparing them to observations of galaxies, clusters and other large-scale structures. This truly ground-breaking work puts the study of modified gravity models on the same footing as the standard model of cosmology. Since the discovery of the accelerating expansion of the Universe, marked by the awarding of the 2011 Nobel Prize in Physics, there has been a growing interest in understanding what drives that acceleration. One possible explanation lies in theories of gravity beyond Einstein’s General Relativity. This thesis addresses all aspects of the problem, an approach that is crucial to avoiding potentially catastrophic biases in the interpretation of upcoming observational missions.