Dark matter (DM) constitutes almost 85% of all mass able to cluster into gravitationally bound objects. Thus it has played the determining role in the origin and evolution of the structure in the universe often referred to as the Cosmic Web. The dark matter component of the Cosmic Web or simply the Dark Matter Web is considerably easier to understand theoretically than the baryonic component of the web if one assumes that DM interacts only gravitationally. One of the major differences between the DM and baryonic webs consists in the multi stream structure of the DM web. Thus it allows to use three diagnostic fields that do not present in the baryonic web: the number of streams field in Eulerian space, the number of flip flops field in Lagrangian space, and the caustic structure in the both. Although these characteristics have been known for a long time their systematic studies as fields started only a few years ago. I will report new recent results of numerical studies of the three fields mentioned above and also discuss the features of the DM web they have unveil.[-]

Cosmological N-body simulations are one of the most versatile tools for studying the evolution of large-scale structure in the Universe. While the Newtonian limit of general relativity can be used for most purposes within the basic LCDM model, the true nature of the dark components (dark matter and dark energy) is unknown and may ultimately require a relativistic description. Also the neutrinos from the standard model are relativistic for most of the cosmic history if they have a mass within the range allowed by cosmological and laboratory constraints. In this course I will introduce a framework for relativistic N-body simulations that can treat any relativistic degrees of freedom self-consistently. Furthermore, I will discuss the important aspect of how the simulation data are mapped to observables by constructing the past light cone of an observation event. As an instructive example the effect of massive neutrinos will be the subject of two Hands-on sessions, where I will demonstrate how to use the relativistic N-body code gevolution.
• Lecture 1 — The spacetime of N-body simulations
• Lecture 2 — Observables on the light cone
• Hands-on 1 — The matter power spectrum with massive neutrinos
• Hands-on 2 — Weak lensing with massive neutrinos[-]

Current estimations of cosmological parameters depend often on assumptions about the cosmological model itself. The estimates of $H_{0}$ or $\Omega_{m}$ from CMB surveys, for instance, are valid only assuming a particular model, typically the standard $\Lambda$CDM. Similar model-dependent results are obtained also from analyses of large-scale structure. In some case it is however possible to combine observations in such a way to get estimates of physical quantities that are valid regardless (to some extent) of the underlying model. Here I will discuss how one can determine the cosmological expansion rate $H(z)$ and the deviation from Einstein gravity $\eta$ by combining in a model-independent way several observational probes, from redshift distortions, to lensing, to matter clustering.[-]

In these lectures we give a general introduction to the theory of gravitational waves and the analytic approximation methods in general relativity. More precisely we focus on the theory which is necessary to accurately and reliably predict the gravitational waves generated by compact binary systems, made of black holes or neutron stars. The predictions are used in the form of gravitational-wave “templates” in the data analysis of the detectors LIGO, VIRGO, ... LISA. In particular we present the state-of-the-art on the post-Newtonian approximation in general relativity, which is the main tool for describing the famous gravitational wave “chirp” of compact binary systems. The outline of the lectures is :
1. Gravitational wave events
2. Methods to compute gravitational waves
3. Einstein quadrupole formalism
4. Post-Newtonian parameters
5. Finite size effects in compact binaries
6. Synergy with the effective field theory
7. Radiation reaction and balance equations. [-]

In this course I will give an overview of different line of sight and environmental effects that are expected to modify/distort a gravitational wave (GW) signal emitted by an astrophysical source at cosmological distance. After an overview of the state of the art of GW observations, I will review the derivation of the waveform emitted by a binary system of compact objects in a flat background, in the newtonian approximation. I will then consider a cosmological context and introduce the concept of standard siren. Finally I will derive which is the expected distortion of an emitted waveform induced by the presence of peculiar velocities and (strong) gravitational lensing.

Lecture 1 — Gravitational waves–introduction
Lecture 2 — Gravitational waves–propagation effects in waveform modeling[-]

Recent years have seen the development of a range of modified gravity theories to tackle the dark energy and cosmological constant problem. An interesting class of such models are those in which the graviton effectively becomes massive, modifying gravity at large (cosmological) distances without changing physics at solar system and smaller scales. Such effective field theories have the Vainshtein mechanism built in, and are closely associated with Galileon theories.

In these lectures I will give a brief general overview of both soft and hard massive gravity theories, their origin from extra dimensional models, and the special class of ghost-free massive gravity models and their extensions with multiple massive (and massless) spin-2 states. I will review the Vainshtein mechanism, and the decoupling limits of these theories and how they are related to Galileons. I will then discuss a variety of implications of such theories.

• lecture 1: I will introduce the description of massless and massive spin-2 states, and explain how theseemerge naturally in extra dimensional models, and go on to give the description of so-called ghost-freeor $\Lambda_{3}$ theories of interacting massive spin-2 fields, aka massive gravity and its multi-gravity extensions.

• lecture 2: I will review some aspects of the phenomenology of the general class of massive gravity theories: screening - cosmology - black hole solutions, and if time go on to discuss more recent extensions which attempt to raise the cutoff, connections with UV completions such as TTbar deformations, and the significance of ‘positivity bounds' applied to these effective theories.[-]