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Ultimo aggiornamento 26 ott 2017
Lumen Boco
Sesso M
Esperimento FLAG
Tipo Laurea Magistrale
Destinazione dopo il cons. del titolo Dottorato (Italia)
Università Universita' Di Trento
Titolo The role of Yang-Mills fields in Higgs inflation
Abstract The expansion of the universe is accelerated: Riess and Perlmutter, in 1998, found observational evidences of that, observing type IA supernovae, respectively in the "High-z SN Search Team" and "Supernova Cosmology Project". Their luminosity distance, at a given red-shift, was larger than expected for a decelerating universe; the only way to explain such observation was to admit the universe acceleration. This fact, initially, appeared quite strange, since the only force acting on cosmic scales is gravity which is supposed to be attractive, if the strong energy condition holds. So, if we want to remain in the framework of general relativity, we should add in the cosmological model an exotic form of energy, called dark energy, which, violating the strong energy condition, allows an accelerated expansion. There are also other observational evidences confirming the existence of dark energy: The age of the universe: a computation of the current age of the universe gives a result in contrast with stellar formation theory if you do not consider dark energy contribution in the calculation. Cosmic Microwave Background (CMB) observations: Observations of the CMB anisotropies power spectrum, especially the position of the first peak, tells us clearly that the universe is almost flat. However, in a model with only baryons and dark matter, it is di cult to explain such flatness. Matter power spectrum: The power spectrum of density perturbations has a bell shape; for small k perturbations the power spectrum grows almost linearly, for large k it falls down quadratically, where k is the inverse of the wavelength of the perturbation. The turning point is keq, the scale that enters inside the Hubble horizon at the time of matter-radiation equivalence. The position of keq is di erent if a model with both dark energy and matter is considered with respect to a model with only matter. Experimental data are better fitted by the model which includes also dark energy. Even before dark energy was discovered, it was believed that an accelerated exponential expansion should have been happened in the early universe: inflation. Indeed the standard cosmological model has some internal contradictions and issues, which could be summarized in 3 principal problems: Flatness problem: CMB observations show us that the universe is almost flat. However, studying dynamically the evolution of the curvature, it is possible to see that it tends to increase with time. This means that the universe should have been even more flat in the past. So, in order to have the universe we observe today, we must set the initial curvature almost exactly equal to 0. However, this appear to be a fine-tuning of the initial conditions, we would prefer to have a physical mechanism which could explain such flatness. Horizon problem: CMB homogeneity and isotropy gives a strong support to the cosmological principle, but it hides something very weird: computing the horizon size at the time of last scattering, we find that it was of about 0.4 Mpc, corresponding to an angle of 2 in our sky. Last scattering surface can be divided in about 20000 patches of the horizon size. But, in every direction, a measure of the CMB photons temperature gives always the same result: T 2.725 K. Thus a question arises quite naturally: how could the CMB have such an homogeneous temperature if all these patches have never had time to communicate with each other? Monopole problem: it is not only a cosmological problem but also a particle physics one. GUT theories predicts, after the spontaneous symmetry breaking of the SU(5) symmetry, the creation of point-like topological defects, the magnetic monopoles. Studying their dynamics in a cosmological context, it can be proven that they should have more energy density than all the rest of the matter in the universe, but how it is possible since we have never seen neither one magnetic monopole? Inflation is an elegant solution for all the three problems, as we will see in the thesis. So, in the modern cosmological paradigm, there are two phases of accelerated expan- sion, one happened in the early universe and one at late times. For what concerns late time cosmic acceleration, the model which better fits observational data is CDM, where the cosmological constant , which acts as a vacuum energy, plays the role of dark energy. However there are also other models based on scalar fields, called quintessence models, which try to explain this phenomenon. For what concerns inflation, the most popular models are, again, based on a scalar field (the inflaton), which, under certain conditions, can drive the initial exponential expansion. However both quintessence and inflaton fields are not included in the standard model of particle physics (SM), and, if not found, they weaken the models based on them, since they seem inserted just to explain incomprehensible phenomena. From the theoretical point of view, it could be much better if such fields were already present in the SM. An interesting work, from which I took inspiration for this thesis, identifies the scalar field responsible for the late time cosmic acceleration with the standard model Higgs field, coupled to the SO(3) Yang-Mills field. It proves that acceleration can arise dynamically, with the Higgs potential which acts as a cosmological constant. This is a great result, since it does not need to introduce a cosmological constant or a field beyond the standard model. However this model fails in the early universe dynamics, since it does not predicts inflation. Also for inflation there is a model which identify the inflaton with the Higgs field: Higgs inflation. However, in this case, Higgs field is non minimally coupled to gravity and the interactions with the other SM fields are neglected, since they are usually considered unable to change the inflationary dynamics. But, for what we know, there is no proof, in the literature, of that. So, in order to improve Higgs inflation model, we considered a new lagrangian including the interaction of the Higgs field with the SO(3) Yang-Mills one, also in the hope to reconcile Higgs inflation and Higgs dark energy models under a unique physical explanation. So we studied if, including the interaction, inflation is preserved and which are the constraints that inflationary paradigm imposes on the standard model parameters. In Chapter 1 we will briefly explain the cosmological principle, deriving from that the structure of the universe (Friedman-Lemaitre-Robertson-Walker (FLRW) metric) and its dynamics. Then we will show the evidences for the existence of dark energy, and finally we will analyze some dark energy models, explaining their advantages and disadvantages. In Chapter 2, we will come back to the problems of the standard cosmological model and we will explain them more quantitatively, showing also how inflation can solve them. Then we will deepen the inflation dynamics, explaining the three main formu- lations of it: old, new and chaotic inflation. We will also analyze the cosmological linear perturbation theory and define the spectral indices. Finally we will present the Higgs inflation model. In Chapter 3, after a brief introduction on gauge symmetries and Yang-Mills fields, we will try to include the interaction between the Higgs and the SO(3) Yang-Mills field in the Higgs inflation model, in order to see if it can provide a viable model for inflation or if it spoils it completely.
Anno iscrizione
Data conseguimento 25 ott 2017
Luogo conseguimento Trento
Massimiliano Rinaldi   
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