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Ultimo aggiornamento 26 ott 2017
Autore
Alessandro Casalino
Sesso M
Esperimento FLAG
Tipo Laurea Magistrale
Destinazione dopo il cons. del titolo Dottorato (Italia)
Università Universita' Di Trento
Strutt.INFN/Ente
TIFPA
Titolo Cosmological perturbation in Horndeski gravity: a case study
Abstract In the last few years, new promising theories have been developed in cosmology: the Modified General Relativity theories. As we can guess from the name, these theories involves the modification of the standard General Relativity equations. Although they increase the complexity of cosmology problems, and open new challenges in the mathematical modelling of cosmological models, the Modified General Relativity theories promise to explain more convincingly some current mysteries of large scale physics, among which there are the existence of dark matter and dark energy. On the other hand, we will see that we must pay a greater attention with respect to General Relativity, since the greater complexity in Modified General Relativity models might introduce new stability problems that can make a model unsuitable for describing the universe at large scales. Moreover, in the past few years many observations analysed the presence of anisotropies of the photon distribution and the inhomogeneities of the matter density in the universe. Among the most important experiments that gathered these data, there is the Planck experiment of 2015 [3]. In the next years a new important experiment will start, the Euclid experiment of the European Space Agency [5]. The theoretical background used to explain inhomogeneities and anisotropies makes use of a perturbation theory on the metric and the matter components densities, and is based on a complex set of coupled di?erential equations that are not analytically solvable. In order to validate these theories, in addition to the theoretical framework, it is therefore necessary to find a way to compare e ciently analytical results coming from the theory and experimental results coming from the observations mentioned above. The increasing complexity of these theoretical models imposes a standard approach in order to compare theory and observations, using software that com- pute cosmological parameters, like the age of the universe or the Hubble parameter, and perturbation quantities like the already mentioned CMB. These software are based on a perturbation theory on the metric and on the cosmic matter density. Since we can not directly compare the action (which defines a Modified General Relativity theory) with observations, in cosmology is impossible to find experimental quantities that can be directly compared with the theoretical models, and therefore it is necessary to use these software. In this thesis we will firstly make an introduction of the standard cosmology starting from General Relativity (Chapter I). With these tools we will study the history of the universe, focusing on the cosmological epochs and events (Chapter 2). These epochs and events greatly a?ect the theory we will introduce in the next chapter, the perturbation theory used in cosmology to model inhomogeneities in the matter density in the universe and anisotropies in the radiation distribution (Chapter 3). We will consider only a first order perturbation theory in small perturbation functions, but in principle higher order are necessary to explain the structure growth of cosmic bodies. We will also show some of the main result (Cosmic Microwave Background and power spectral density of the matter) for the standard model of cosmology ?CDM (Chapter 4). We will then apply this theory to the study of one software, CLASS, and its Modified General Relativity extension, hi class, where the latter was also developed by E. Bellini (Chapter 5). We will then introduce the Modified General Relativity, in particular a subset of theories called Horndeski gravity, with a particular attention on the problem of General Relativity that this theory can solve (Chapter 6). We will also show the main results for the perturbation theory in Horndeski gravity, and we will explore the results for one of the simplest model: the Quintessence. Finally, we will consider a specific sector of Horndeski gravity that mimics the dark matter at background level, as recently studied by M. Rinaldi, and compare the numerical results with observations (Chapter 7). We will find that this model experience instabilities in the perturbation functions, that makes it unsuitable for explaining the anisotropies of the radiation distribution and inhomogeneities of the matter density in the universe.
Anno iscrizione
Data conseguimento 25 ott 2017
Luogo conseguimento Trento
Relatore/i
Massimiliano Rinaldi   
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