Aspects of Leptogenesis Scenarios at Grand Unification and Sub-TeV Scales and Their Possible Low-Energy Tests

In the present Thesis, we investigate various aspects of leptogenesis scenarios based on the type-I seesaw extension of the Standard Model (SM) with 2, 3 heavy Majorana neutrinos $N_j$ with masses $M_j$, $j = 1,\,...,\,3$, as well as the possibilities to test the scenarios considered by us in currently running and/or future planned low-energy experiments. We focus first on the high-scale leptogenesis framework with strongly hierarchical mass spectrum of the heavy Majorana neutrinos, namely $M_1$ << $M_2$ << $M_3$, with $M_1$ in the range $(10^{8}-10^{14})$ GeV, concentrating on the possibility that the requisite CP-violation for the generation of the baryon asymmetry of the Universe $\eta_B$ is provided solely by the low-energy Dirac and/or Majorana phases of the light neutrino mixing (PMNS) matrix. A detailed numerical analysis of the solution to the quantum density matrix equations in this scenario, performed with the powerful ULYSSES code we have developed, reveals a number of novel features: i) $\eta_B$ going through zero and changing sign at the transitions between different flavour regimes (1-to-2 and 2-to-3) in the case of vanishing initial abundance of $N_1$ and strong wash-out effects; ii) inadequate description of the transitions between different flavour regimes by the corresponding Boltzmann equations; iii) flavour effects persisting beyond $10^{12}$ GeV and making it possible to reproduce the observed value of $\eta_B$ at these high-scales even though the CP-violation is provided only by the Dirac and/or Majorana phases of the PMNS matrix. Considering the somewhat simpler case of just two heavy Majorana neutrinos $N_{1,\,2}$ (with the heaviest $N_3$ decoupled) we show that relatively large part of the viable leptogenesis parameter space can be probed in low-energy neutrino experiments. We find, in particular, that, when the CP-violation is provided exclusively by the Dirac phase $\delta$ of the PMNS matrix, there is a correlation between the sign of $\sin\delta$ and the sign of $\eta_B$. This opens up the possibility to test part of the parameter space of this scenario in low-energy experiments on CP-violation in neutrino oscillations. A measurement of the Dirac and/or Majorana phases would also constrain the range of scales for which one can have viable leptogenesis in the considered scenario. Next, we show that in the low-scale resonant leptogenesis scenario with two heavy Majorana neutrinos $N_{1,\,2}$ forming a pseudo-Dirac pair, with $M\simeq M_{1,\,2}$ and a small mass splitting $| M_2-M_1 |$ << $M$, the observed $\eta_B$ can be reproduced for $M$ in the range $(0.1\sim 100)$ GeV by relying only on the decay mechanism, either during the production ("freeze-in") or departure from equilibrium ("freeze-out") of $N_{1,\,2}$. In this context, the inclusion of flavour and thermal effects in the formalism of Boltzmann equations is crucial for predicting the observed value of $\eta_B$. Also, we find that the viable parameter space of this resonant scenario is compatible with values of the heavy Majorana neutrino couplings to the SM that could be probed at future colliders, like at the discussed FCC-ee facility. When low-scale leptogenesis with three quasi-degenerate in mass heavy Majorana neutrinos $N_{1,\,2,\,3}$ with $M\simeq M_{1,\,2,\,3}$ is considered in the formalism of density matrix equations and, in particular, with both the heavy Majorana neutrino oscillation and decay mechanisms taken into account, the viable parameter space for $M$ in the range $(0.05-7\times 10^4)$ GeV enlarges considerably and becomes accessible to direct searches at the LHC, as well as in fixed target experiments and future colliders. We demonstrate that planned and upcoming experiments on charged lepton flavour violating processes with muons $\mu^\pm$, specifically MEG II on $\mu\to e\gamma$ decay, Mu3e on $\mu \to eee$ decay, Mu2e and COMET on $\mu - e$ conversion in aluminium and PRISM/PRIME on $\mu - e$ conversion in titanium, can test significant region of the viable leptogenesis parameter space and may potentially establish the first hint of such low-scale leptogenesis scenario.