Cosmology has been transformed by dramatic progress in high-precision observations and theoretical modelling. This book surveys key developments and open issues for graduate students and researchers. Using a relativistic geometric approach, it focuses on the general concepts and relations that underpin the standard model of the Universe. Part I covers foundations of relativistic cosmology whilst Part II develops the dynamical and observational relations for all models of the Universe based on general relativity. Part III focuses on the standard model of cosmology, including inflation, dark matter, dark energy, perturbation theory, the cosmic microwave background, structure formation and gravitational lensing. It also examines modified gravity and inhomogeneity as possible alternatives to dark energy. Anisotropic and inhomogeneous models are described in Part IV, and Part V reviews deeper issues, such as quantum cosmology, the start of the universe and the multiverse proposal. Colour versions of some figures are available at www.cambridge.org/9780521381154.

This book presents more than 200 problems, with detailed guided solutions, spanning key areas of particle physics and astrophysics. The selected examples enable students to gain a deeper understanding of these fields and also offer valuable support in the preparation for written examinations. The book is an ideal companion to Introduction to Particle and Astroparticle Physics: Multimessenger Astronomy and its Particle Physics Foundations, written by Alessandro De Angelis and Mario Pimenta and published in its second edition in Springer's Undergraduate Lecture Notes in Physics series in 2018. It can, however, also be used independently. The present book is organized into 11 chapters that match exactly those in the companion textbook, and each of the exercises is given a title to facilitate identification of the subject within that book. Some new exercises have been added because they are considered helpful on the basis of the experience gained by teachers while using the textbook. Beyond students on relevant courses, exercises and solutions in particle and astroparticle physics are of value for physics teachers and to all who seek aid to self-training.

Rather than focusing on the contributions of theoretical physicists to the understanding of the subatomic world and of the beginning of the universe - as most popular science books on particle physics do - this book is different in that, firstly, the main focus is on machine inventors and builders and, secondly, particle accelerators are not only described as discovery tools but also for their contributions to tumour diagnosis and therapy. The characters of well-known (e.g. Ernest Lawrence) and mostly unknown actors (e.g. Nicholas Christofilos) are outlined, including many colourful quotations. The overall picture supports the author's motto: "Physics is beautiful and useful". Advance appraisal: "Accelerators go all the way from the unique and gargantuan Large Hadron Collider to thousands of smaller versions in hospitals and industry. Ugo Amaldi has experience across the range. He has worked at CERN and has for many years been driving the application of accelerators in medicine. This is a must-read introduction to this frontier of modern technology, written beautifully by a world expert." Frank Close, Professor of Physics at Oxford University author of "The Infinity Puzzle" "This book should be read by school teachers and all those interested in the exploration of the microcosm and its relation to cosmology, and in the use of accelerators for medical applications. With a light hand and without formulae the autho r easily explains complicated matters, spicing up the text with amusing historical anecdotes. His reputation as an outstanding scientist in all the fields treated guarantees high standards." Herwig Schopper, former CERN Director General author of "LEP - The Lord of the Collider Rings at CERN" "This book tells the story of modern physics with an unusual emphasis on the machine-builders who made it all possible, and their machines. Learning to accelerate particles has enabled physicists to probe the subatomic world and gain a deeper understanding of the cosmos. It has also brought numerous benefits to medicine, from the primitive X-ray machines of over a century ago to today's developments in hadron therapy for cancer. Amaldi tells this story in a most fascinating way." Edward Witten, Professor of Mathematical Physics at the Institute for Advanced Study in Princeton; Fields Medal (1990)

With a focus on modified gravity this book presents a review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. General Relativity and the CDM framework are currently the standard lore and constitute the concordance paradigm of cosmology. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology in the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. In this review all extended theories and scenarios are first examined under the light of theoretical consistency, and are then applied in various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology has been able to offer in the last two decades. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature, allowing readers to get a clear overview of the state of the art and where the field of modified gravity is likely to go. This work was performed in the framework of the COST European Action "Cosmology and Astrophysics Network for Theoretical Advances and Training Actions" - CANTATA.

This thesis is devoted to the systematic study of non-local theories that respect Lorentz invariance and are devoid of new, unphysical degrees of freedom. Such theories are attractive for phenomenological applications since they are mostly unconstrained by current experiments. Non-locality has played an increasingly important role in the physics of the last decades, appearing in effective actions in quantum field theory, and arising naturally in string theory and non-commutative geometry. It may even be a necessary ingredient for quantum theories of gravity. It is a feature of quantum entanglement, and may even solve the long-standing black hole information loss problem. "Non-locality" is a broad concept with many promising and fruitful applications in theoretical and mathematical physics. After a historical and pedagogical introduction into the concept of non-locality the author develops the notion of non-local Green functions to study various non-local weak-field problems in quantum mechanics, quantum field theory, gravity, and quantum field theory in curved spacetime. This thesis fills a gap in the literature by providing a self-contained exploration of weak-field effects in non-local theories, thereby establishing a "non-local intuition" which may serve as a stepping stone for studies of the full, non-linear problem of non-locality.

Owing to the increased accuracy requirements in fields such as astrometry and geodesy the general theory of relativity must be taken into account for any mission requiring highly accurate orbit information and for practically all observation and measurement techniques. This book highlights the confluence of Applied Mathematics, Physics and Space Science as seen from Einstein's general theory of relativity and aims to bridge the gap between theoretical and applied domains. The book investigates three distinct areas of general relativity: Exact solutions of the Einstein field equations of gravitation. Dynamics of near-Earth objects and solar system bodies. Relativistic orbitography. This book is an updated and expanded version of the author's PhD thesis which was awarded the International Astronomical Union PhD prize in Division A: Fundamental Astronomy. Included is a new introduction aimed at graduate students of General Relativity and extended discussions and results on topics in post-Newtonian dynamics and general relativistic spacecraft propagation.

The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin 1/2 and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe. This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.

Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required.

Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations. Summary boxes encapsulate some of the most important results for quick reference. Applications covered include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance.

Aimed at advanced undergraduates with background knowledge of classical mechanics and electricity and magnetism, this textbook presents both the particle dynamics relevant to general relativity, and the field dynamics necessary to understand the theory. Focusing on action extremization, the book develops the structure and predictions of general relativity by analogy with familiar physical systems. Topics ranging from classical field theory to minimal surfaces and relativistic strings are covered in a homogeneous manner. Nearly 150 exercises and numerous examples throughout the textbook enable students to test their understanding of the material covered. A tensor manipulation package to help students overcome the computational challenge associated with general relativity is available on a site hosted by the author. A link to this and to a solutions manual can be found at www.cambridge.org/9780521762458.

A host of astrophysical measurements suggest that most of the matter in the Universe is an invisible, nonluminous substance that physicists call "dark matter." Understanding the nature of dark matter is one of the greatest challenges of modern physics and is of paramount importance to our theories of cosmology and particle physics. This text explores one of the leading hypotheses to explain dark matter: that it consists of ultralight bosons forming an oscillating field that feebly interacts with light and matter. Many new experiments have emerged over the last decade to test this hypothesis, involving state-of-the-art microwave cavities, precision nuclear magnetic resonance (NMR) measurements, dark matter "radios," and synchronized global networks of atomic clocks, magnetometers, and interferometers. The editors have gathered leading experts from around the world to present the theories motivating these searches, evidence about dark matter from astrophysics, and the diverse experimental techniques employed in searches for ultralight bosonic dark matter. The text provides a comprehensive and accessible introduction to this blossoming field of research for advanced undergraduates, beginning graduate students, or anyone new to the field, with tutorials and solved problems in every chapter. The multifaceted nature of the research - combining ideas and methods from atomic, molecular, and optical physics, nuclear physics, condensed matter physics, electrical engineering, particle physics, astrophysics, and cosmology - makes this introductory approach attractive for beginning researchers as well as members of the broader scientific community. This is an open access book.

The book is about exact space-time models of the gravitational fields produced by gravitational radiation. The authors' extensive work in the field is reviewed in order to stimulate the study of such models, that have been known for a long time, and to highlight interesting physical aspects of the existing models in some novel detail. There is an underlying simplicity to the gravitational radiation studied in this book. Apart from the basic assumption that the radiation has clearly identifiable wave fronts, the gravitational waves studied are directly analogous to electromagnetic waves. The book is meant for advanced students and researchers who have a knowledge of general relativity sufficient to carry out research in the field.

Black Holes are regions of space-time where the gravitational field is so strong that not even light can escape. There has been much written on black holes, however in most cases they are treated as isolated objects. The author has found a number of cases in which the interaction of a black hole with another strong-field system (such as the background universe or another black hole) could be treated analytically. This includes using the powerful method of matched asymptotic expansions. In this book the author considers these wider ranging problems and examples for the first time. This book will be widely read by all those working in gravitation, and PhD students in mathematical physics.

Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravity. The Principia is, in fact, a model for all mathematical physics.

Representing a decade's work from one of the world's most distinguished physicists, this major publication is, as far as is known, the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breathtaking economy of Newton's methods. Chandrasehkar's work is an attempt by a distinguished practising scientist to read and comprehend the enormous intellectual achievement of the Principia. This book will stimulate great interest and debate among the scientific community, illuminating the brilliance of Newton's work under the steady gaze of Chandrasekhar's rare perception.

The purpose of this book is to illustrate some of the most important techniques which are helpful in combinatorial problems when computing quantum effects in covariant theories, like general relativity. In fact, most of the techniques find application also in broader contexts, such as low energy effective (chiral) Lagrangians or even in specific problems in condensed matter. Some of the topics covered are: the background field approach and the heat kernel ideas. The arguments are explained in some detail and the presentation is meant for young researchers and advanced students who are starting working in the field. As prerequisite the reader should have attended a course in quantum field theory including Feynman's path integral. In the Appendix a nontrivial calculation of one-loop divergences in Einstein-Hilbert gravity is explained step-by-step.

Starting out from humankind's earliest ideas about the cosmos, this book gives the reader a clear overview of our current understanding of the universe, including big bang theories and the formation of stars and galaxies, as well as addressing open questions. The author shows how our present view gradually developed from observations, and also how the outcome of ongoing research may still change this view. The book brings together concepts in physics and astronomy, including some history in both cases. The text is descriptive rather than technical: the goal is to present things rigorously and without oversimplification, by highlighting the crucial physical concepts. The only prerequisite is a qualitative knowledge of basic physics concepts at high-school level.

A quirky, funny, and accessible blend of science and art that delves into the heart of Einstein’s theory of relativity

It was a link to Albert Einstein’s 1905 paper―an early attempt at explaining his revolutionary ideas on space, time, and matter―that drew Tanya Bub into his imaginative vision of the world. What particularly struck her was how Einstein interwove words and math to create clear visuals illustrating his theories. As an artist, she naturally started doodling as she worked her way through his concepts, creating drawings that intuitively demonstrated Einstein’s core principles.

In Reimagining Time, Tanya Bub teams up with her father, the distinguished physicist Jeffrey Bub, to create a quirky and accessible take on one of science’s most revolutionary discoveries. Blending original art and text, they guide readers―even nonmathematicians―through Einstein’s theory of special relativity to reveal truths about our universe: time is relative, lengths get shorter with motion, energy and mass are interchangeable, and the universe has a speed limit.

Of all philosophers of the 20th century, few built more bridges between academic disciplines than Karl Popper. He contributed to a wide variety of fields in addition to the epistemology and the theory of scientific method for which he is best known. This book illustrates and evaluates the impact, both substantive and methodological, that Popper has had in the natural and mathematical sciences. The topics selected include quantum mechanics, evolutionary biology, cosmology, mathematical logic, statistics, and cognitive science. The approach is multidisciplinary, opening a dialogue across scientific disciplines and between scientists and philosophers.

Offers an accessible text and reference (a cosmic-ray manual) for graduate students entering the field and high-energy astrophysicists will find this an accessible cosmic-ray manual Easy to read for the general astronomer, the first part describes the standard model of cosmic rays based on our understanding of modern particle physics. Presents the acceleration scenario in some detail in supernovae explosions as well as in the passage of cosmic rays through the Galaxy. Compares experimental data in the atmosphere as well as underground are compared with theoretical models

This thesis provides a comprehensive view of the physics of charmed hadrons in high-energy proton-proton and heavy-ion collisions. Given their large masses, charm quarks are produced in the early stage of a heavy-ion collision and they subsequently experience the full system evolution probing the colour-deconfined medium called quark-gluon plasma (QGP) created in such collisions. In this thesis, the mechanisms of charm-quark in-medium energy loss and hadronisation are discussed via the measurements of the production of charm mesons with (Ds+) and without (D+) strange-quark content in different colliding systems, using data collected by the ALICE experiment at the CERN LHC. The participation of the charm quark and its possible thermalisation in the QGP are studied via measurements of azimuthal anisotropies in the production of D+ mesons. Finally, the prospects for future measurements with the upgraded ALICE experimental apparatus and with more refined machine learning techniques are presented.

This book highlights the review of articles in theoretical physics by the students of Professor K. Babu Joseph, as a Festschrift for his 80th Birthday. This book is divided into four sections based on the contributions of Babu Joseph and his students. The four sections are Cosmology, High Energy Physics, Mathematical Physics and Non-linear Dynamics and its applications.

This book collates papers presented at two international conferences (held at the Australian National University in 2018 and Birkbeck College London in 2019) exploring the relationships between big history and astrobiology and their wider implications for society. These two relatively new academic disciplines aim to integrate human history with the wider history of the universe and the search for life elsewhere. The book will show that, despite differences in emphasis, big history and astrobiology share much in common, especially their interdisciplinary approaches and the cosmic and evolutionary perspectives that they both engender. Specifically, the book addresses the unified, all-embracing, nature of knowledge, the impact of big history on humanity and the world at large, the possible impact of SETI on astrobiology and big history, the cultural signature of Earth's inhabitants beyond our own planet, and the political implications of a planetary worldview. The principal readership is envisaged to comprise scholars working in the fields of astrobiology, big history and space exploration interested in forging interdisciplinary links between these diverse topics, together with educators, and a wider public, interested in the societal implications of the cosmic and evolutionary perspectives engendered by research in these fields.

This book presents Special Relativity in a language accessible to students while avoiding the burdens of geometry, tensor calculus, space-time symmetries, and the introduction of four vectors. The search for clarity in the fundamental questions about Relativity, the discussion of historical developments before and after 1905, the strong connection to current research topics, many solved examples and problems, and illustrations of the material in colloquial discussions are the most significant and original assets of this book. Importantly for first-time students, Special Relativity is presented such that nothing needs to be called paradoxical or apparent; everything is explained. The content of this volume develops and builds on the book Relativity Matters (Springer, 2017). However, this presentation of Special Relativity does not require 4-vector tools. The relevant material has been extended and reformulated, with additional examples and clarifications. This introduction of Special Relativity offers conceptual insights reaching well beyond the usual method of teaching relativity. It considers relevant developments after the discovery of General Relativity (which itself is not presented), and advances the reader into contemporary research fields. This presentation of Special Relativity is connected to present day research topics in particle, nuclear, and high intensity pulsed laser physics and is complemented by the current cosmological perspective. The conceptual reach of Special Relativity today extends significantly further compared even to a few decades ago. As the book progresses, the qualitative and historical introduction turns into a textbook-style presentation with many detailed results derived in an explicit manner. The reader reaching the end of this text needs knowledge of classical mechanics, a good command of elementary algebra, basic knowledge of calculus, and introductory know-how of electromagnetism.

Presenting the history of space-time physics, from Newton to Einstein, as a philosophical development DiSalle reflects our increasing understanding of the connections between ideas of space and time and our physical knowledge. He suggests that philosophy's greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time and motion, and the roles they play in our assumptions about physical objects and physical measurements. This way of thinking leads to interpretations of the work of Newton and Einstein and the connections between them. It also offers ways of looking at old questions about a priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy.

This book presents the superfield description of various supersymmetric field theory models in three- and four-dimensional space-times. A mapping between superfield and component formulations of supersymmetric field theories is discussed. The author also describes the methodology for calculating quantum corrections in these theories employing supergraph formalism and functional methods, and illustrates these approaches with many detailed examples of how such calculations are performed for various superfield models.