Forecasts on the dark energy anisotropic stress for the esa euclid survey

The cosmological constant Λ seems to be a not satisfactory explanation of the late-time accelerated expansion of the Universe, for which a number of experimental evidences exist; therefore, it has become necessary in the last years to consider alternative models of dark energy, meant as cause of the accelerated expansion. In the study of dark energy models, it is important to understand which quantities can be determined starting from observational data, without assuming any hypothesis on the cosmological model; such quantities have been determined in Amendola, Kunz et al., 2012. In the same paper it has been further shown that it is possible to estabilish a relation between the model-independent parameters and the anisotropic stress η, which can be also expressed as a combination of the functions appearing in the most general Lagrangian for the scalar-tensor theories, the Horndeski Lagrangian. In the present thesis, the Fisher matrix formalism is used to perform a forecast on the constraints that will be possible to make on the anisotropic stress η in the future, starting from the estimated uncertainties for the galaxy clustering and weak lensing measurements which will be performed by the European Space Agency Euclid mission, to be launched in 2020. Further, constraints coming from supernovae-Ia observations are considered. The forecast is performed for two cases in which (a) η is considered as depending from redshift only and (b) η is constant and equal to one, as in the ΛCDM model.

Color/kinematic duality, double copies and scalar matrix models

In questa tesi presentiamo una descrizione autoconsistente della dualità Colore/Cinematica nelle teorie di gauge e al processo di Double Copy. Particolare attenzione viene data all'approccio alla dualità con il formalismo di cono-luce, in quanto semplifica notevolmente sia il calcolo sia l'interpretazione fisica: vengono indagati i settori duale e self-duale per poi passare al modello di Chalmers e Siegel per l'estensione alla teoria generale. Proponiamo quindi uno Scalar Matrix Model, che può essere un buon modello per generare ampiezze ottenibili da una Double Copy `inversa', e ne studiamo un'eventuale dualità a la Colore/Cinematica. Vengono illustrati alcuni casi particolari di rottura spontanea di simmetria. In appendice riportiamo un notebook di Mathematica per il calcolo di ampiezze tree level di puro gauge, utile per i calcoli necessari allo studio della dualità.

Cosmological predictions for a scalar tensor dark energy model by a dedicated Einstein-Boltzmann code

We have extended the Boltzmann code CLASS and studied a specific scalar tensor dark energy model: Induced Gravity

Properties of cosmic voids in dark energy simulations

The last decade has witnessed the establishment of a Standard Cosmological Model, which is based on two fundamental assumptions: the first one is the existence of a new non relativistic kind of particles, i. e. the Dark Matter (DM) that provides the potential wells in which structures create, while the second one is presence of the Dark Energy (DE), the simplest form of which is represented by the Cosmological Constant Λ, that sources the acceleration in the expansion of our Universe. These two features are summarized by the acronym ΛCDM, which is an abbreviation used to refer to the present Standard Cosmological Model. Although the Standard Cosmological Model shows a remarkably successful agreement with most of the available observations, it presents some longstanding unsolved problems. A possible way to solve these problems is represented by the introduction of a dynamical Dark Energy, in the form of the scalar field ϕ. In the coupled DE models, the scalar field ϕ features a direct interaction with matter in different regimes. Cosmic voids are large under-dense regions in the Universe devoided of matter. Being nearby empty of matter their dynamics is supposed to be dominated by DE, to the nature of which the properties of cosmic voids should be very sensitive. This thesis work is devoted to the statistical and geometrical analysis of cosmic voids in large N-body simulations of structure formation in the context of alternative competing cosmological models. In particular we used the ZOBOV code (see ref. Neyrinck 2008), a publicly available void finder algorithm, to identify voids in the Halos catalogues extraxted from CoDECS simulations (see ref. Baldi 2012 ). The CoDECS are the largest N-body simulations to date of interacting Dark Energy (DE) models. We identify suitable criteria to produce voids catalogues with the aim of comparing the properties of these objects in interacting DE scenarios to the standard ΛCDM model, at different redshifts. This thesis work is organized as follows: in chapter 1, the Standard Cosmological Model as well as the main properties of cosmic voids are intro- duced. In chapter 2, we will present the scalar field scenario. In chapter 3 the tools, the methods and the criteria by which a voids catalogue is created are described while in chapter 4 we discuss the statistical properties of cosmic voids included in our catalogues. In chapter 5 the geometrical properties of the catalogued cosmic voids are presented by means of their stacked profiles. In chapter 6 we summarized our results and we propose further developments of this work.

Mean curvature flow in SE (2) and applications to visual perception

Our goal in this thesis is to provide a result of existence of the degenerate non-linear, non-divergence PDE which describes the mean curvature flow in the Lie group SE(2) equipped with a sub-Riemannian metric. The research is motivated by problems of visual completion and models of the visual cortex.