Abstract: A plausible explanation for the lightness of neutrino masses is that neutrinos are massless at tree level, with their mass (typically Majorana) being generated radiatively at one or more loops. The new couplings, together with the suppression coming from the loop factors, imply that the new degrees of freedom cannot be too heavy (they are typically at the TeV scale). Therefore, in these models there are no large mass hierarchies and they can be tested using different searches, making their detailed phenomenological study very appealing. In particular, the new particles can be searched for at colliders and generically induce signals in lepton-flavor and lepton-number violating processes (in the case of Majorana neutrinos), which are not independent from reproducing correctly the neutrino masses and mixings. The main focus of the review is on Majorana neutrinos. We order the allowed theory space from three different perspectives: (i) using an effective operator approach to lepton number violation, (ii) by the number of loops at which the Weinberg operator is generated, (iii) within a given loop order, by the possible irreducible topologies. We also discuss in more detail some popular radiative models which involve qualitatively different features, revisiting their most important phenomenological implications. Finally, we list some promising avenues to pursue.

Abstract: Cosmological observables show a dependence with the neutrino mass, which is partially degenerate with parameters of extended models of gravity. We study and explore this degeneracy in Horndeski generalized scalar-tensor theories of gravity. Using forecasted cosmic microwave background and galaxy power spectrum datasets, we find that a single parameter in the linear regime of the effective theory dominates the correlation with the total neutrino mass. For any given mass, a particular value of this parameter approximately cancels the power suppression due to the neutrino mass at a given redshift. The extent of the cancellation of this degeneracy depends on the cosmological large-scale structure data used at different redshifts. We constrain the parameters and functions of the effective gravity theory and determine the influence of gravity on the determination of the neutrino mass from present and future surveys.

Abstract: We study the impact of stochastic noise on the generation of primordial black hole (PBH) seeds in ultra-slow-roll (USR) inflation with numerical simulations. We consider the non-linearity of the system by consistently taking into account the noise dependence on the inflaton perturbations, while evolving the perturbations on the coarse-grained background affected by the noise. We capture in this way the non-Markovian nature of the dynamics, and demonstrate that non-Markovian effects are subleading. Using the Delta N formalism, we find the probability distribution P(R) of the comoving curvature perturbation R. We consider inflationary potentials that fit the CMB and lead to PBH dark matter with i) asteroid, ii) solar, or iii) Planck mass, as well as iv) PBHs that form the seeds of supermassive black holes. We find that stochastic effects enhance the PBH abundance by a factor of O(10)-O(10(8)), depending on the PBH mass. We also show that the usual approximation, where stochastic kicks depend only on the Hubble rate, either underestimates or overestimates the abundance by orders of magnitude, depending on the potential. We evaluate the gauge dependence of the results, discuss the quantum-to-classical transition, and highlight open issues of the application of the stochastic formalism to USR inflation.