Abstract: Recent constrains on the sum of neutrino masses inferred by analyzing cosmological data, show that detecting a non-zero neutrino mass is within reach of forthcoming cosmological surveys. Such a measurement will imply a direct determination of the absolute neutrino mass scale. Physically, the measurement relies on constraining the shape of the matter power spectrum below the neutrino free streaming scale: massive neutrinos erase power at these scales. However, detection of a lack of small-scale power from cosmological data could also be due to a host of other effects. It is therefore of paramount importance to validate neutrinos as the source of power suppression at small scales. We show that, independent on hierarchy, neutrinos always show a footprint on large, linear scales; the exact location and properties are fully specified by the measured power suppression (an astrophysical measurement) and atmospheric neutrinos mass splitting (a neutrino oscillation experiment measurement). This feature cannot be easily mimicked by systematic uncertainties in the cosmological data analysis or modifications in the cosmological model. Therefore the measurement of such a feature, up to 1% relative change in the power spectrum for extreme differences in the mass eigenstates mass ratios, is a smoking gun for confirming the determination of the absolute neutrino mass scale from cosmological observations. It also demonstrates the synergy between astrophysics and particle physics experiments.

Abstract: The phase diagram of quantum chromodynamics is conjectured to have a rich structure containing at least three forms of matter: hadronic nuclear matter, quarkyonic matter and quark-gluon plasma. We justify the origin of the quarkyonic phase transition in a chiral-quark model and describe its formulation in terms of Skyrme crystals.

Abstract: Motivated by discrete flavour symmetry models, we analyse Spontaneous CP Violation (SCPV) for potentials involving three or six Higgs fi elds (both electroweak doublets and singlets) which fall into irreducible triplet representations of discrete symmetries belonging to the Delta(3n(2)) and Delta(6n(2)) series, including A(4), S-4, Delta(27) and Delta(54). For each case, we give the potential and fi nd various global minima for di ff erent regions of the parameter space of the potential. Using CP-odd basis Invariants that indicate the presence of Spontaneous CP Violation we separate the VEVs into those that do or do not violate CP. In cases where CP is preserved we reveal a CP symmetry of the potential that is preserved by those VEVs, otherwise we display a non-zero CP-odd Invariant. Finally we identify interesting cases where there is Spontaneous Geometrical CP Violation in which the VEVs have geometrical phases.