We propose a minimal seesaw extension to simultaneously account for realistic neutrino mass and mixing, the baryon asymmetry of the Universe via leptogenesis and a viable dark matter relic density, in which two right-handed neutrinos are coupled to a dark Dirac fermion and complex scalar field, both charged under a global U (1)D symmetry. As a concrete example, we consider the Littlest Seesaw model which describes neutrino mass and mixing and accounts for leptogenesis, thereby fixing the neutrino Yukawa couplings and right-handed neutrino masses. By considering the freezein production mechanism of dark matter, we explore the parameter space of right-handed neutrino portal couplings and dark particle masses which give the correct dark matter relic abundance, focussing on the case of a superheavy Dirac fermion dark matter particle, with a mass around 10 10 GeV. Such a FIMPzilla can provide a successful explanation of the dark matter relic abundance, with its production reliant on neutrino Yukawa couplings over much of the parameter space, depending on the assumed dark particle masses, and the reheat temperature. CONTENTS

In the so-called Planckian Interacting Dark Matter (PIDM) scenario, superheavy dark matter particles are produced after inflation by gravity-mediated interactions through the freeze-in mechanism. In the minimal PIDM model, the absence of any additional direct coupling with Standard Model particles is assumed. However, for scalar dark matter particles there is no symmetry that suppresses the Higgs portal coupling. In this paper, we therefore study the impact of a non-zero interaction with the Higgs field on the PIDM paradigm for scalar dark matter. In particular, we fully explore the model parameter space in order to identify the allowed regions where the correct dark matter abundance is achieved. Moreover, we provide the threshold value for the Higgs portal coupling below which the corresponding production processes are sub-dominant and the minimal PIDM scenario is preserved. For a benchmark scalar dark matter mass of 10 15 GeV, we find that the Higgs portal coupling has to be smaller than 5.1 × 10 −8 (1.1 × 10 −7 ) for instantaneous (non-instantaneous) reheating.

In the classic type I seesaw mechanism with very heavy right-handed (RH) neutrinos, it is possible to account for dark matter via RH neutrino portal couplings to a feebly interacting massive particle (FIMP) dark sector. However, for large RH neutrino masses, gravity can play an important role. We study the interplay between the neutrino portal through the right-handed neutrinos and the gravity portal through the massless spin-2 graviton in producing dark matter particles in the early universe. As a concrete example, we consider the minimal and realistic Littlest Seesaw model with two RH neutrinos, augmented with a dark scalar and a dark fermion charged under a global U (1)D dark symmetry. In the model, the usual seesaw neutrino Yukawa couplings and the right-handed neutrino masses (the lightest being about 5 × 10 10 GeV) are fixed by neutrino oscillations data and leptogenesis. Hence, we explore the parameter space of the two RH neutrino portal couplings, the two dark particle masses and the reheating temperature of the universe, where the correct dark matter relic abundance is achieved through the freeze-in mechanism. In particular, we highlight which class of processes dominate the dark matter production. We find that, despite the presence of the gravity portal, the dark matter production relies on the usual seesaw neutrino Yukawa coupling in some regions of the parameter space, so realising a direct link between dark matter and neutrino phenomenology. Finally, we report the threshold values for the neutrino portal couplings below which the neutrino portal is irrelevant and the Planckian Interacting Dark Matter paradigm is preserved.

We consider a minimal type Ib seesaw model where the effective neutrino mass operator involves two different Higgs doublets, and the two right-handed neutrinos form a heavy Dirac mass. We propose a minimal dark matter extension of this model, in which the Dirac heavy neutrino is coupled to a dark Dirac fermion and a dark complex scalar field, both charged under a discrete Z2 symmetry, where the lighter of the two is a dark matter candidate. Focussing on the fermionic dark matter case, we explore the parameter space of the seesaw Yukawa couplings, the neutrino portal couplings and dark scalar to dark fermion mass ratio, where correct dark matter relic abundance can be produced by the freeze-in mechanism. By considering the mixing between the standard model neutrinos and the heavy neutrino, we build a connection between the dark matter production and current laboratory experiments ranging from collider to lepton flavour violating experiments. For a GeV mass heavy neutrino, the parameters related to dark matter production are constrained by the experimental results directly and can be further tested by future experiments such as SHiP.

We consider a minimal non-supersymmetric SO(10) Grand Unified Theory (GUT) model that can reproduce the observed fermionic masses and mixing parameters of the Standard Model. We calculate the scales of spontaneous symmetry breaking from the GUT to the Standard Model gauge group using two-loop renormalisation group equations. This procedure determines the proton decay rate and the scale of U(1)B−L breaking, which generates cosmic strings and the right-handed neutrino mass scales. Consequently, the regions of parameter space where thermal leptogenesis is viable are identified and correlated with the fermion masses and mixing, the neutrinoless double beta decay rate, the proton decay rate, and the gravitational wave signal resulting from the network of cosmic strings. We demonstrate that this framework, which can explain the Standard Model fermion masses and mixing and the observed baryon asymmetry, will be highly constrained by the next generation of gravitational wave detectors and neutrino oscillation experiments which will also constrain the proton lifetime.