Introduction to Gravitational Lensing

PART I: Generalities

1. Light deflection

1.1. Deflection of a light corpuscle

1.2. Deflection of light according to General Relativity

1.3. Deflection by an ensable of point masses

1.4. Deflection by an extended mass distribution

1.5. Light propagation through an inhomogeneous universe

1.6. Python examples

2. The general lens

2.1. Lens equation

2.2. Lensing potential

2.3. First order lens mapping

2.4 Magnification

2.5 Lensing to the second order

2.6 Time delay surface

2.7 Python examples

PART II: Applications of gravitational lensing

1. Microlensing

1.1 The point mass lens

1.2 Standard microlensing light curve

1.3 Microlensing parallax

1.4 Optical depth and event rate

1.5 Astrometric microlensing

1.6 Multiple point lenses

1.7 Planetary microlensing

1.8 Python examples

2. Strong lensing by galaxies and galaxy clusters

2.1 Axially symmetric lenses

2.2 Power-law lens

2.3 Softened lenses

2.4 Elliptical lenses

2.5 Substructures

2.6 External shear

2.7 Parametric lens modeling

2.8 Non-parametric lens modeling

2.9 Searches for strong lenses

2.10 Cosmic telescopes

2.11 Strong lensing cosmography

2.12 Time-delay cosmology

2.13 Python examples

3. Weak lensing by virialized structures

3.1 Shear measurements

3.2 Tangential and cross component of the shear

3.3 Lens mass measurements

3.4 Two-dimensional mass mapping

3.5 Mass-sheet degeneracy

3.6 Python examples

4. Weak lensing by the large-scale-structure

4.1 Effective convergence

4.2 Limber's equation

4.3 Shear correlation functions

4.4 Shear in apertures and aperture mass

4.5 E- and B-modes

4.6 Python examples

5. Lensing of the Cosmic Microwave Background

5.1 Lensing of the CMB temperature

5.2 Gravitational lensing of the CMB polarization

5.3 Recovery of the gravitational potential

5.4 Python examples

Massimo Meneghetti is a researcher at INAF, Observatory of Astrophysics and Space Science of Bologna, Italy. He obtained his Ph.D. in Astronomy at the University of Padova and worked at the Institute for Theoretical Astrophysics of the University of Heidelberg (Germany) and at the Jet Propulsion Laboratory in Pasadena (USA). His research focuses on cosmology and structure formation to understand the nature of dark matter and dark energy, the major components of the Universe, topics on which he has authored over 160 papers. In particular, he has taken major roles in several international projects that use gravitational lensing as a tool to investigate the matter distribution in cosmic structures like galaxies and galaxy clusters and to explore the distant universe. He taught gravitational lensing to master students in Astrophysics and Cosmology at the University of Bologna for more than ten years, during this period he developed the lecture notes contained in this book.