Harmonic Analysis of Linear Fields on the Nilgeometric Cosmological Model

To analyze linear field equations on a locally homogeneous spacetime by means of separation of variables, it is necessary to set up appropriate harmonics according to its symmetry group. In this paper, the harmonics are presented for a spatially compactified Bianchi II cosmological model -- the nilgeometric model. Based on the group structure of the Bianchi II group (also known as the Heisenberg group) and the compactified spatial topology, the irreducible differential regular representations and the multiplicity of each irreducible representation, as well as the explicit form of the harmonics are all completely determined. They are also extended to vector harmonics. It is demonstrated that the Klein-Gordon and Maxwell equations actually reduce to systems of ODEs, with an asymptotic solution for a special case.Comment: 28 pages, no figures, revised version to appear in JM

The effect of supersymmetry breaking in the Mass Varying Neutrinos

We discuss the effect of the supersymmetry breaking on the Mass Varying Neutrinos(MaVaNs) scenario. Especially, the effect mediated by the gravitational interaction between the hidden sector and the dark energy sector is studied. A model including a chiral superfield in the dark sector and the right handed neutrino superfield is proposed. Evolutions of the neutrino mass and the equation of state parameter are presented in the model. It is remarked that only the mass of a sterile neutrino is variable in the case of the vanishing mixing between the left-handed and a sterile neutrino on cosmological time scale. The finite mixing makes the mass of the left-handed neutrino variable.Comment: 6 pages, 7 figures, RevTeX4, references added, discussions and figures revise

Cosmological Family Asymmetry and CP violation

We discuss how the cosmological baryon asymmetry can be achieved by the lepton family asymmetries of heavy Majorana neutrino decays and they are related to CP violation in neutrino oscillation, in the minimal seesaw model with two heavy Majorana neutrinos. We derive the most general formula for CP violation in neutrino oscillation in terms of the heavy Majorana masses and Yukawa mass term. It is shown that the formula is very useful to classify several models in which $e-$, $\mu-$ and $\tau-$leptogenesis can be separately realized and to see how they are connected with low energy CP violaton. To make the models predictive, we take texture with two zeros in the Dirac neutrino Yukawa matrix. In particular, we find some interesting cases in which CP violation in neutrino oscillation can happen while lepton family asymmetries do not exist at all. On the contrary, we can find $e-$, $\mu-$ and $\tau-$leptogenesis scenarios in which the cosmological CP violation and low energy CP violation measurable via neutrino oscillations are very closely related to each other. By determining the allowed ranges of the parameters in the models, we predict the sizes of CP violation in neutrino oscillation and $|V_{e3}^{MNS}|$. Finally, the leptonic unitarity triangles are reconstructed.Comment: 22 pages, 9 figures A figure caption correcte

Tri-bimaximal Mixing and Cabibbo Angle in S4 Flavor Model with SUSY

We present a flavor model of quarks and leptons with the non-Abelian discrete symmetry $S_4$ in the framework of the SU(5) SUSY GUT. Three generations of $\bar 5$-plets in SU(5) are assigned to ${\bf 3}$ of $S_4$ while the first and second generations of 10-plets in SU(5) are assigned to ${\bf 2}$ of $S_4$, and the third generation of 10-plet is assigned to ${\bf 1}$ of $S_4$. Right-handed neutrinos are also assigned to ${\bf 2}$ for the first and second generations and ${\bf 1}'$ for the third generation. We predict the Cabibbo angle as well as the tri-bimaximal mixing of neutrino flavors. We also predict the non-vanishing $U_{e3}$ of the neutrino flavor mixing due to higher dimensional mass operators. Our predicted CKM mixing angles and the CP violation are consistent with experimental values. We also study SUSY breaking terms in the slepton sector. Our model leads to smaller values of flavor changing neutral currents than the present experimental bounds.Comment: 32 pages, 4 figures, some references are added, with minor modificatio

Examining the Geometrical Model with Inverted Mass Hierarchy for Neutrinos

The comprehensive analyses are presented in the model with the inverted mass hierarchy for neutrinos, which follows from a geometrical structure of a (1+5) dimensional space-time where two extra dimensions are compactified on the T^2/Z_3 orbifold. The model gives two large lepton flavor mixings due to the S3 structure in the (1+5) dimensional space-time. It also predicts the lightest neutrino mass as m_3=(1-50)\times 10^{-5}eV and the effective neutrino mass responsible for neutrinoless double beta decays as _{ee}\simeq 50 meV. The low energy CP violation, J_{CP} could be 0.02. On the other hand, the observed baryon asymmetry in the present universe is produced by the non-thermal leptogenesis, which works even at the reheating temperature TR=10^{4}-10^{6}GeV. The correlation between the baryon asymmetry and the low energy CP violation is examined in this model.Comment: 17 pages, 10 figures, a reference is added, minor change in introductio

Scalar fields on SL(2,R) and H^2 x R geometric spacetimes and linear perturbations

Using appropriate harmonics, we study the future asymptotic behavior of massless scalar fields on a class of cosmological vacuum spacetimes. The spatial manifold is assumed to be a circle bundle over a higher genus surface with a locally homogeneous metric. Such a manifold corresponds to the SL(2,R)-geometry (Bianchi VIII type) or the H^2 x R-geometry (Bianchi III type). After a technical preparation including an introduction of suitable harmonics for the circle-fibered Bianchi VIII to separate variables, we derive systems of ordinary differential equations for the scalar field. We present future asymptotic solutions for these equations in a special case, and find that there is a close similarity with those on the circle-fibered Bianchi III spacetime. We discuss implications of this similarity, especially to (gravitational) linear perturbations. We also point out that this similarity can be explained by the "fiber term dominated behavior" of the two models.Comment: 23 pages, no figures, to be published in Class. Quant. Gravi

Seasonal cycles of ozone and oxidized nitrogen species in northeast Asia - 2:A model analysis of the roles of chemistry and transport

[1] The dominant factors controlling the seasonal variations of ozone (O-3) and three major oxidized nitrogen species, peroxyacetyl nitrate (PAN), nitrogen oxides (NOx), and nitric acid (HNO3), in northeast Asia are investigated by using a three-dimensional global chemical transport model to analyze surface observations made at Rishiri Island, a remote island in northern Japan. The model was evaluated by comparing with observed seasonal variations, and with the relationships between O-3, CO, and PAN. We show that the model reproduces the chemical environment at Rishiri Island reasonably well, and that the seasonal cycles of O-3, CO, NOy species, and VOCs are well predicted. The impact of local emissions on some of these constituents is significant, but is not the dominant factor affecting the seasonal cycles. The seasonal roles of chemistry and transport in controlling O-3 and PAN are revealed by examining production/ destruction and import/ export/deposition fluxes in the boundary layer over the Rishiri region. For O-3, transport plays a key role throughout the year, and the regional photochemical contribution is at most 10% in summer. For PAN, in contrast, transport dominates in winter, while in-situ chemistry contributes as much as 75% in summer. It is suggested that the relative contribution of transport and in-situ chemistry is significantly different for O-3 and PAN, but that the wintertime dominance of transport due to the long chemical lifetimes of these species is sufficient to drive the seasonal cycles of springtime maximum and summertime minimum characteristic of remote sites