This book introduces the phenomenology of gravitational lensing in an accessible manner and provides a thorough discussion of the related astrophysical applications. It is intended for advanced undergraduates and graduate students who want to start working in this rapidly evolving field. This includes also senior researchers who are interested in ongoing or future surveys and missions such as DES, Euclid, WFIRST, LSST. The reader is guided through many fascinating topics related to gravitational lensing like the structure of our galaxy, the searching for exoplanets, the investigation of dark matter in galaxies and galaxy clusters, and several aspects of cosmology, including dark energy and the cosmic microwave background. The author, who has gained valuable experience as academic teacher, guides the readers towards the comprehension of the theory of gravitational lensing and related observational techniques by using simple codes written in python. This approach, beyond facilitating the understanding of gravitational lensing, is preparatory for learning the python programming language which is gaining large popularity both in academia and in the private sector.

This book brings together reviews from leading international authorities on the developments in the study of dark matter and dark energy, as seen from both their cosmological and particle physics side. Studying the physical and astrophysical properties of the dark components of our Universe is a crucial step towards the ultimate goal of unveiling their nature. The work developed from a doctoral school sponsored by the Italian Society of General Relativity and Gravitation. The book starts with a concise introduction to the standard cosmological model, as well as with a presentation of the theory of linear perturbations around a homogeneous and isotropic background. It covers the particle physics and cosmological aspects of dark matter and (dynamical) dark energy, including a discussion of how modified theories of gravity could provide a possible candidate for dark energy. A detailed presentation is also given of the possible ways of testing the theory in terms of cosmic microwave background, galaxy redshift surveys and weak gravitational lensing observations. Included is a chapter reviewing extensively the direct and indirect methods of detection of the hypothetical dark matter particles. Also included is a self-contained introduction to the techniques and most important results of numerical (e.g. N-body) simulations in cosmology. " This volume will be useful to researchers, PhD and graduate students in Astrophysics, Cosmology Physics and Mathematics, who are interested in cosmology, dark matter and dark energy.

This book presents gravitational lensing as an essential tool in astrophysics for tracking dark matter at all scales in the Universe.

In this work, mainly aimed at teachers of physics, mathematics and astronomy, it is illustrated how two important topics of cosmology can be introduced as valuable teaching aids: the dark matter problem and gravitational lensing. These complex and articulated topics have been treated with appropriate elementarisation and the use of simplified models, that made them suitable for introduction into the classroom in the form of exercises and/or extracurricular projects for students in their final years of secondary school or first years of university. In the first part of this thesis, the concepts of radial and rotational velocity, together with those of spider diagram and rotation curve, are introduced and applied to the solar system and a spiral galaxy. The inclusion of the spider diagram in this educational context is innovative. All this is discussed while working with real data and using the dynamic mathematical software Geogebra. Finally, we estimate the amount of non-visible mass that apparently influences the motion of all matter in a spiral galaxy. This provides evidence for the possible existence of dark matter. In the second part, we discuss the phenomenon of strong gravitational lensing, which can produce optical illusions observable in the universe. This effect is investigated for several examples of mass distributions acting as lenses. By examining the geometry of the gravitational lens system, we deduce size, distances and alignment of the components. Using this information and thanks to the software Geogebra, visualisations and interactive simulations of the images resulting from the gravitational lensing effect are created. Finally, the form to be given to lenses made of glass, to recreate the same effects produced by gravitational lenses, is studied. We have designed and produced five models of plexiglass lenses, that add an experimental part to the teaching of this subject, as they reproduce the gravitational lens effect directly in the classroom.

A unique graduate textbook that develops powerful approximation methods and their applications to real-life astrophysical systems.

This textbook provides an introduction to gravitational lensing, which has become an invaluable tool in modern astrophysics, with applications that range from finding planets orbiting distant stars to understanding how dark matter and dark energy conspired to form the cosmic structures we see today. Principles of Gravitational Lensing begins with Einstein’s prediction that gravity bends light, and shows how that fundamental idea has spawned a rich field of study over the past century. The gravitational deflection of light was first detected by Eddington during a solar eclipse in May 1919, launching Einstein and his theory of relativity into public view. Yet the possibility of using the phenomenon to unlock mysteries of the Universe seemed remote, given the technology of the day. Theoretical work was carried out sporadically over the next six decades, but only with the discovery of the system Q0957+561 in 1979 was gravitational lensing transformed from a curiosity of general relativity into a practical observational tool. This book describes how the three subfields known as strong lensing, weak lensing, and microlensing have grown independently but become increasingly intertwined. Drawing on their research experience, Congdon and Keeton begin with the basic physics of light bending, then present the mathematical foundations of gravitational lensing, building up to current research topics in a clear and systematic way. Relevant background material from physics and mathematics is included, making the book self-contained. The derivations and explanations are supplemented by exercises designed to help students master the theoretical concepts as well as the methods that drive current research. An extensive bibliography guides those wishing to delve more deeply into particular areas of interest. Principles of Gravitational Lensing is ideal for advanced students and seasoned researchers looking to penetrate this thriving subject and even contribute research of their own.

Best-selling, accessible physics-first introduction to GR uses minimal new mathematics and begins with the essential physical applications.