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PubblicazioneWandering around the walls of Super-QCD(SISSA, 2021-09-17)In this thesis, we consider supersymmetric domain walls of four-dimensional N=1 super-QCD for the simply connected gauge groups Sp(N) and SU(N). First, we construct the BPS domain walls numerically when the number of flavors F=N, N+1 in the SU(N) case, and F=N+1, N+2 in the Sp(N) case. In the second part, we discuss some proposals for the low energy descriptions of the physics on the domain walls. These proposals pass various tests, including dualities and matching of the vacua of the massive 3d theory with the 4d analysis. However, our analysis is partially successful in some cases. In those cases, we suggest that new purely quantum phenomena are needed to properly describe the low energy physics.
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PubblicazioneBeyond Perturbation Theory in Cosmology(SISSA, 2021-09-16)Over many years, our current understanding of the Universe has been extremely relied on perturbation theory (PT) both theoretically and experimentally. There are, however, many situations in cosmology in which the analysis beyond PT is required. In this thesis we study three examples: the resonant decay of gravitational waves (GWs), the dark energy (DE) instabilities induced by GWs, and the tail of the primordial field distribution function. The first two cases are within the context of the Effective Field Theory (EFT) of DE, whereas the last one is within inflation. We first review the construction of the EFT of DE, which is the most general Lagrangian for the scalar and tensor perturbations around the flat FLRW metric. Specifically, this EFT can be mapped to the covariant theories, known as Horndeski and Beyond Horndeski theories. We then study the implications on the dark energy theories coming from the fact that GWs travel with the speed $c_T = 1$ at LIGO/Virgo frequencies. After that, we consider the perturbative decay of GWs into DE fluctuations ($gamma ightarrow pipi$) due to the $ ilde{m}_4^2$ operator. This process is kinematically allowed by the spontaneous breaking of Lorentz invariance. Therefore, having no perturbative decay of gravitons together with $c_T = 1$ at LIGO/Virgo, rules out all quartic and quintic beyond Horndeski theories. As the first non-perturbative regime in this thesis, we study the decay of GWs into DE fluctuations $pi$, taking into account the large occupation numbers of gravitons. When the $m_3^3$ (cubic Horndeski) and $ ilde{m}_4^2$ (beyond Horndeski) operators are present, the GW acts as a classical background for $pi$ and modifies its dynamics. In particular, $pi$ fluctuations are described by a Mathieu equation and feature instability bands that grow exponentially. In the regime of small GW amplitude which corresponds to narrow resonance, we calculate analytically the produced $pi$, its energy and the change of the GW signal. Eventually, the resonance is affected by $pi$ self-interactions in a way that we cannot describe analytically. The fact that $pi$ self-couplings coming from the $m_3^3$ operator become quickly comparable with the resonant term affects the growth of $pi$ so that the bound on $alpha_{ m B}$ remains inconclusive. However, in the case of the $ ilde{m}_4^2$ operator self-interactions can be neglected at least in some regimes. Therefore, our resonant analysis improves the perturbative bounds on $alpha_{ m H}$, ruling out quartic Beyond Horndeski operators. In the second non-perturbative regime we show that $pi$ may become unstable in the presence of a GW background with sufficiently large amplitude. We find that dark-energy fluctuations feature ghost and/or gradient instabilities for GW amplitudes that are produced by typical binary systems. Taking into account the populations of binary systems, we conclude that the instability is triggered in the whole Universe for $|alpha_{ m B}| gtrsim 10^{-2}$, i.e. when the modification of gravity is sizable. The fate of the instability and the subsequent time-evolution of the system depend on the UV completion, so that the theory may end up in a state very different from the original one. In conclusion, the only dark-energy theories with sizable cosmological effects that avoid these problems are $k$-essence models, with a possible conformal coupling with matter. In the second part of the thesis we consider physics of inflation. Inflationary perturbations are approximately Gaussian and deviations from Gaussianity are usually calculated using in-in perturbation theory. This method, however, fails for unlikely events on the tail of the probability distribution: in this regime non-Gaussianities are important and perturbation theory breaks down for $|zeta| gtrsim |f_{ m NL}|^{-1}$. We then show that this regime is amenable to a semiclassical treatment, $hbar ightarrow 0$. In this limit the wavefunction of the Universe can be calculated in saddle-point, corresponding to a resummation of all the tree-level Witten diagrams. The saddle can be found by solving numerically the classical (Euclidean) non-linear equations of motion, with prescribed boundary conditions. We apply these ideas to a model with an inflaton self-interaction $propto lambda dot{zeta}^4$. Numerical and analytical methods show that the tail of the probability distribution of $zeta$ goes as $exp(-lambda^{1/4}zeta^{3/2})$, with a clear non-perturbative dependence on the coupling. Our results are relevant for the calculation of the abundance of primordial black holes.
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PubblicazioneRelativistic accretion disk models for Active Galactic Nuclei: mass and spin of Supermassive black holes(SISSA, 2021-09-17)Active Galactic Nuclei are among the brightest and most energetic objects in the Universe and determining their mass M and spin a is crucial for understanding their physical nature, the link with the host galaxy, and their possible evolution in time. The commonly accepted scenario describes them with a supermassive black hole of 10^6 − 10^10 solar masses at their center along with an accretion disk of hot rotating matter. The surrounding environment (e.g., dusty torus, Broad and Narrow Line Region) is thought to be shaped by both the strong gravitational field of the black hole and the disk radiation. Uncertainties on their mass and spin are still too large and new methods have to be used to set more stringent constraints. In this thesis, I used different accretion disk models to predict the main black hole features (i.e., mass and spin), comparing them with different independent measurements, and to study the surrounding environment (i.e., the dusty torus), shaped by the relativistic disk radiation pattern.
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PubblicazioneComplementary probes of the nature of dark matter(SISSA, 2021-09-16)There is overwhelming evidence for the existence of a nonbaryonic dark matter (DM) component in the Universe's energy budget, coming from various astrophysical and cosmological probes, but its nature is very much unknown. A plethora of models have been proposed, mostly under the umbrella of the particle DM paradigm. The desired properties of DM indicates that it is only natural to expect that a viable DM candidate lies in extensions of the Standard Model (SM). In this work, we have considered minimal models that address the so-called DM puzzle, which are also motivated by theoretical issues and experimental anomalies in the SM. Firstly, motivated by the possibility that the nonbaryonic component could be described by a dark sector framework that is as complex as the SM, we consider a scenario in which DM resides in a multicomponent dark sector. The stable species are charged under an unbroken U(1) dark force, mediated by a massless dark photon, and they also interact with ordinary matter through scalar portals. We study its implications on cosmology, by studying its early Universe evolution through the numerical solution of a set of Boltzmann equations which track the relic densities and the temperatures of the dark and visible sectors. On the other hand, the reported discrepancy between the SM prediction and the recently announced experimental measurement of the muon magnetic dipole moment is addressed from the point of view of new physics. Here we introduced a minimal model, inspired by the MSSM, where the bino-like Majorana fermion is regarded as the DM candidate, while other species such as the sleptons are necessary to both alleviate the tension in the muon g-2, as well as to produce the correct relic density of DM. Meanwhile, the attempt to understand the nature of DM is not only limited to tracking its early Universe history nor to provide solutions to experimental anomalies, but also by probing it in relaxed structures, that have formed at late times, such as the halo in our own Milky Way (MW) galaxy. DM in the MW halo can be probed through direct detection searches, which rely on observing possible recoil signals induced by scatterings of DM with nuclei or with electrons. Deriving direct detection limits on DM requires the calculation of the theoretical recoil signal, which involves specifying the elementary interaction of DM with ordinary matter, as well as properly assessing the systematic uncertainties coming from nuclear physics, atomic physics, and astrophysics. Here we focus on quantifying the astrophysical uncertainty which enters in the assumption for the velocity distribution of DM in the MW. We advocate the implementation of equilibrium axisymmetric modeling to describe the DM phase space distribution function (PSDF). This has the advantage of being self-consistent with the MW mass model, which is axisymmetric and is well-supported by latest kinematic data on tracers of the underlying MW gravitational potential. We assess the impact of the axisymmetric PSDF particularly on DM-electron scattering, which is an excellent probe of sub-GeV DM, and compare the resulting exclusion limits coming from the Standard Halo Model (SHM) that is often quoted in the literature.
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PubblicazioneAspects of the Modular Symmetry Approach to Lepton Flavour(SISSA, 2021-09-16)A new bottom-up approach to the flavour problem based on modular invariance has been recently proposed and has gained considerable attention in the literature. In the present thesis we develop basic aspects of the requisite modular symmetry formalism and explore its application to the lepton flavour problem. After introducing the relevant notions (the modular group, the modulus field and modular forms), we concentrate on the theoretical tools required for model-building such as explicit construction of the modular forms, the interplay of modular and CP transformations and of the related symmetries, classification of residual symmetries and their possible relation to the observed hierarchical flavour patterns. Armed with these tools, we construct and discuss three examples of viable models of lepton flavour: a simple predictive model depending on a small number of parameters, a model with an unbroken residual symmetry which leads to trimaximal neutrino mixing, and a model with a slightly broken residual symmetry which explains the observed pattern of charged-lepton masses without fine-tuning.
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