Search

In this thesis, we study new aspects of flavour model building in the context of supersymmetric Grand Unified Theories, where the focus lies on models with an SU(5) or SO(10) gauge group. In the framework of supergravity, we discuss how a typical flavon sector of a flavour model with spontaneously broken family symmetry can be combined with a SUSY breaking sector in a consistent manner. To demonstrate the predictive power of such an implementation, an example calculation for a flavour GUT model, which is based on an SU(5) gauge group, an A_4 family symmetry and a Z^R_4 R-symmetry, is performed. Assuming hidden sector SUSY breaking, we determine the structure of the soft SUSY breaking terms at the GUT scale and investigate the predictions for observables at low energy scales, such as the sparticle spectrum, the dark matter relic density and flavour violating processes. Next, we carry out a systematic analysis of a class of predictive SU(5) flavour GUT models with the CSD2 setup in the neutrino sector, and where the ratios of the Yukawa couplings in the down-quark and charged lepton sector are fixed by Clebsch-Gordan coefficients at the GUT scale, following the principle of single operator dominance. Alongside the identification of viable model candidates by performing a fit to experimental data for different combinations of CG coefficients, we calculate, among others, the predictions for the 2-3 mixing angle theta^PMNS_23 and the CP violating phase delta^PMNS in the lepton sector. In the context of SO(10) Grand Unification, a class of non-renormalizable Yukawa operators of the schematic form 16_I 16_J H 45^n 210^m is investigated, where H in {10,120,126bar} contains SU(2)_L doublet and antidoublet states, and 16_I,J the SM fermions. Moreover, the representations 45 and 210 acquire SM singlet vevs at the GUT scale. We provide general formulas to compute the resulting Yukawa couplings in the different fermion sectors of the MSSM, and discuss the construction of such operators from renormalizable interactions by using heavy mediators. In addition, we show that the alignment of the MSSM Higgs (anti)doublets H_u and H_d in the space of all SU(2)_L (anti)doublets of a concrete model is a central aspect for the prediction of Yukawa ratios at the GUT scale. Finally, we specify the numerical procedure to quantitatively calculate nucleon decay from dimension 5 operators in SUSY models, and apply the analysis to an example model with an SU(5) GUT symmetry.

In particle physics motivated models of the early universe, non-linear preheating dynamics of scalar fields can give rise to rich phenomenology. An example phenomenon is e.g. the formation of oscillons: quasi-stable, localised, and non-linear scalar field configurations. In the first of three main parts of this thesis we study the gravitational wave (GW) production of asymmetric (ellipsoidal) oscillons in an expanding universe. Based on model-independent, simplifying assumptions on the properties of oscillons, we derive an analytical expression for the anisotropic stress tensor. The latter is subsequently used to numerically compute the stochastic GW background of different "oscillon cosmologies". In particular, we investigate and discuss how different properties of an oscillon cosmology, such as the background expansion or the size, and amplitude of oscillons, manifest themselves in the stochastic background of GWs. The second and third part of this thesis are devoted to lattice studies in which the non-linear scalar field dynamics, as well as the associated production of GWs is explored in different models. In the second part we consider different realisations of a supersymmetric model of hilltop inflation in which an additional scalar field $\chi$ couples to the inflaton. We find that during preheating $\chi$ can get resonantly amplified due to a non-standard parametric resonance that is driven by the dynamics of inhomogeneous inflaton fluctuations. Moreover, we show that qualitative differences in the dynamics of the fields are manifested in the resulting GW background. In the third part we consider the non-linear dynamics of Kähler moduli in two scenarios of moduli stabilisation in type IIB string theory. More explicitly we study the dynamics of the overall volume modulus in the Kachru-Kallosh-Linde-Trivedi (KKLT) scenario, as well as the dynamics of a single blow-up modulus in the Large Volume Scenario (LVS). More specifically, we consider the dynamics of preheating of moduli that get displaced from their post-inflationary minimum through the "vacuum misalignment" mechanism. In both models we show that preheating can be very efficient and lead to the non-linear fragmentation of the moduli and, ultimately, to the formation of oscillons. Interestingly, we find that the dynamics are qualitatively different in the KKLT scenario compared to the dynamics of the blow-up modulus in the LVS. The corresponding differences are also imprinted in the resulting GW background.

The extension of the Standard Model of particle physics by sterile neutrinos can naturally explain the smallness of neutrino masses as observed by neutrino oscillation and nuclear beta decay experiments. These hypothetical particles, also referred to as heavy neutrinos in the mass eigenbasis, can give rise to a testable phenomenology when they have masses around the electroweak scale. Hence they are actively searched for at, for instance, colliders such as the Large Hadron Collider. The proposed future colliders, which are currently in the design phase, will be more powerful than the operated colliders to date. The new possibilities which they provide to search for sterile neutrinos and to test the neutrino mass mechanism in the not too far future have therefore to be assessed. In this thesis, various aspects of the sterile neutrino phenomenology as well as various searches for sterile neutrinos at colliders are investigated. In particular, we study the contributions from sterile neutrinos to the Higgs boson production mechanism at colliders, the implications of long-lived heavy neutrinos that lead to displaced vertex events, lepton-number violation as the manifestation of heavy neutrino-antineutrino oscillations, lepton-flavour violation as the consequence of leptonic mixing, the possibilities to resolve heavy neutrino-antineutrino oscillations, how to test the viable leptogenesis parameter space, and their implications to collider searches. These collider studies are investigated in the context of low scale seesaw scenarios featuring ns = 2 sterile neutrinos with masses in the range of O(1 GeV) and O(1 TeV), which constitutes the benchmark scenario. Within the benchmark scenario, analytical calculations, and analyses of Monte Carlo generated event samples are performed. The investigated collider studies demonstrate promising avenues to test sterile neutrinos at future colliders. This contains novel possible search strategies by the search for Higgs bosons produced from heavy neutrinos and by probing the effects from heavy neutrino-antineutrino oscillations via the displaced vertex search. The assessed capabilities of the future colliders with respect to the sterile neutrino searches contribute to the physics case of the future colliders.

In this thesis, we study supersymmetric models of tribrid inflation and new inflation, both of which can be realized with a tribrid superpotential. In the first part, we focus on tribrid inflation, deriving relations between cosmological observables and model parameters as well as providing guidelines for embedding tribrid inflation in realistic particle physics models. As an example application, we show how tribrid inflation can be realized in an explicit model of the leptonic flavour structure based on a discrete family symmetry, and how the production of topological defects after inflation can be avoided in such a model. Finally, we consider the possibility of generating the non-renormalizable operators of the tribrid superpotential at a sub-Planckian mass scale, which extends the applicability of tribrid inflation to some models with intermediate energy scales. In the second part, we study new inflation with tribrid superpotentials. We first calculate the effects of the imaginary inflaton component on the primordial perturbations, which are generic for supersymmetric realizations of new inflation and not specific to the tribrid superpotential. Afterwards, we show how the tribrid superpotential coupling provides not only a mechanism for dynamically generating the initial conditions for new inflation, but also an effective inflaton decay channel for reheating after inflation. We also study the different preheating mechanisms in this setup and discuss under which conditions preheating can affect the final reheating phase. In the last part, we consider whether small-field models of slow-roll inflation would remain viable if large primordial tensor perturbations were observed. In particular, we explain why such an observation would imply a scale dependent running of the spectral index, and we derive a general slow-roll bound to prove that an observation of tensor modes close to the current upper bound has the potential to rule out the entire framework of small-field slow-roll inflation employed throughout this thesis.

Grand Unified Theories (GUTs) offer an attractive framework for flavour models, since they feature relations between quarks and leptons. Combining them with Supersymmetry (SUSY) and flavour symmetries, we derive predictions for the flavour and SUSY flavour structure from various GUT models and discuss how the double missing partner mechanism (DMPM) solution to the doublet-triplet splitting problem can be combined with predictions for GUT scale quark-lepton Yukawa coupling relations. We construct two predictive SUSY SU(5) GUT models with an A4 flavour symmetry, that feature realistic quark-lepton Yukawa coupling ratios and mixing angle relations. These GUT scale predictions arise after GUT symmetry breaking from a novel combination of group theoretical Clebsch-Gordan factors, and we carefully construct additional shaping symmetries and renormalisable messenger sectors to protect the models' predictions from dangerous corrections. The major difference between both models are their respective predictions of a normal and inverse neutrino mass ordering. We perform Markov Chain Monte Carlo analyses, fit to experimental data, and discuss how the models can be tested by present and future experiments. To combine predictive GUT scale quark-lepton Yukawa coupling ratios with the DMPM in SUSY SU(5), we introduce a second GUT breaking Higgs field in the adjoint representation. Two explicit flavour models with different predictions for the GUT scale Yukawa sector are presented, including shaping symmetries and renormalisable messenger sectors, and combined with the DMPM. We calculate the effective masses of the colour triplets mediating proton decay and find that they can be made sufficiently heavy. In SUSY theories, the one-loop SUSY threshold corrections are of particular importance in investigating GUT scale quark-lepton mass relations and thus link a given GUT flavour model to the sparticle spectrum. We calculate the one-loop SUSY threshold corrections of the full MSSM Yukawa coupling matrices in the electroweak-unbroken phase and introduce a new software tool SusyTC as a major extension to the Mathematica package REAP. Finally we find predictions for the CMSSM parameters and sparticle masses from the GUT scale Yukawa coupling ratios used in the flavour models of this thesis.

In this thesis, we investigate several ways how the structure of a high energy particle physics model constituting a grand unification theory (GUT) in supersymmetry (SUSY) can be inferred from multiple types of information obtained at low energy. First, we calculate the values and 1 sigma ranges of the running quark and lepton Yukawa couplings as well as of the quark mixing parameters at various energy scales to provide useful input for flavour model building in GUTs and other scenarios while including tan beta enhanced SUSY threshold corrections in a simple way. Next, we analyse the naturalness of the Minimal Supersymmetric Standard Model (MSSM) in the light of the discovery of the Higgs boson at the Large Hadron Collider (LHC). In particular, we find that among possible departures from the constrained MSSM (cMSSM) non-universal gaugino masses represent the most promising way to find parameter regions with a fine-tuning of only O(10) even for a Higgs mass of about 126 GeV, compared to O(100) for the cMSSM. In this context, we also discuss the preference for certain GUT-scale Yukawa coupling ratios over others based on fine-tuning. Following that, we study how also the recent determination of the leptonic mixing angle theta^pmns_13 can be accommodated in a simple scenario for GUT models of flavour via charged lepton corrections. This leads us to four conditions that can easily be implemented. In addition, the interplay of the value of theta^pmns_13 with future determinations of the Dirac CP phase delta^pmns is discussed using lepton mixing sum rules. Finally, we study how the double missing partner mechanism as a solution to the doublet-triplet splitting problem can be incorporated into SU(5) GUT models of flavour to comply with the bounds on proton decay. In this context, we argue that the introduction of two adjoints of SU(5) is a compelling idea and calculate its constraints on the GUT scale and dimension five proton decay suppression scale at two loops. We close with general comments on the calculation of the proton lifetime in the considered scenario for flavour models. Multiple appendices are included detailing non-obvious aspects of the calculation and other kinds of valuable information for GUT model building.