Determining the Equation of State of the Expanding Universe Using a New Independent Variable

To determine the equation of state of the universe, we propose to use a new independent variable $R\equiv (H_0/c)(d_L(z)/(1+z))$, where $H_0$ and $d_L(z)$ are the present Hubble parameter and the luminosity distance, respectively. For the flat universe suggested from the observation of the anisotropy of cosmic microwave background, the density and the pressure are expressed as $\rho/\rho_0=4(df/dR)^2/f^6$ and $p/\rho_0=-4/3(d^2f/dR^2)/f^5$ where $\rho_0$ is the present density and $f(R)=1/\sqrt{1+z(R)}$. In $(R, f)$ plane the sign as well as the strength of the pressure is in proportion to the curvature of the curve $f(R)$. We propose to adopt a Pade-like expression of $f(R)=1/\sqrt{u}$ with $u\equiv 1+\sum\limits_{n=1}^{N}u_nR^n$. For flat $\Lambda$ model the expansion up to N=7 has at most an error $< 0.2$ for $z < 1.7$ and any value of $\Lambda$. We also propose a general method to determine the equation of state of the universe which has $N-1$ free parameters. If the number of parameters are smaller than $N-1$, there is a consistency check of the equation of state so that we may confirm or refute each model.Comment: 12 pages, to be published in the Astrophysical Journa

Factors Associated with Choking During Meals; a Risk Indicator for Repetitive Fevers in the Elderly Community

Background: Choking during meals is a common symptom in the elderly, however the factors associated with it have not been fully clarified. In this study, we examined the factors associated with choking during meals. Methods: The oral health status and practices that promote oral health conditions was surveyed in 1305 community dwelling elderly using a self-administered questionnaire. Eight items including satisfaction with their oral condition, denture fit, chewing ability, tooth brushing frequency, dental visits, exercises to train muscles for chewing and swallowing, choking during meals, and repetitive fever were selected for analysis. Results: 25.1% of the subjects experienced choking during meals, which was significantly associated with repetitive fever occurrence. Differences in satisfaction levels with their oral condition, denture fit, chewing ability, and tooth brushing frequency were observed between groups with and without choking. Age, satisfaction level, and chewing ability were significantly associated with choking during meals. Conclusions: This study demonstrated that choking during meals is a risk indicator for repetitive fever in the elderly living in community settings. Poor chewing ability and dissatisfaction with their oral condition were risk factors associated with choking. These results suggest that training the elderly to eat efficiently and safely and improving oral conditions is necessary for those who suffer from choking during meals to prevent repetitive fever. &nbsp

The current problems of the minimal SO(10) GUT and their solutions

This talk consists of two parts. In part I we review how the minimal renormalizable supersymmetric SO(10) model, an SO(10) framework with only one 10 and one 126 Higgs multiplets in the Yukawa sector, is attractive because of its highly predictive power. Indeed it not only gives a consistent predictions on neutrino oscillation data but also gives reasonable and interesting values for leptogenesis, LFV, muon g-2, neutrinoless double beta decay etc. However, this model suffers from problems related to running of gauge couplings. The gauge coupling unification may be spoiled due to the presence of Higgs multiplets much lighter than the grand unification (GUT) scale. In addition, the gauge couplings blow up around the GUT scale because of the presence of Higgs multiplets of large representations. In part II we consider the minimal SO(10) model in the warped extra dimension and show a possibility to solve these problems.Comment: 15 pages, 7 figures, Talk given at the International Workshop on Neutrino Masses and Mixings Toward Unified Understanding of Quarks and Lepton Mass Matrices, held at University of Shizuoka on December 17-19, 200

Time variation of proton-electron mass ratio and fine structure constant with runaway dilaton

Recent astrophysical observations indicate that the proton-electron mass ratio and the fine structure constant have gone through nontrivial time evolution. We discuss their time variation in the context of a dilaton runaway scenario with gauge coupling unification at the string scale $M_{\rm s}$. We show that the choice of adjustable parameters allows them to fit the same order magnitude of both variations and their (opposite) signs in such a scenario.Comment: 16 pages, 1 figure, to appear in Phys. Rev.

Axion and Right-handed Neutrino in the Minimal SUSY SO(10) Model

The connection between the axion and right-handed neutrinos is explored in the framework of the minimal SUSY SO(10) model. The former is related to the Peccei-Quinn (PQ) solution to the strong CP problem and the latter is to the light Majorana neutrinos through the see-saw mechanism. In this model, a relative phase between $({\bf 10,1,3}) (\equiv {\bf \bar{\Delta}}_R) \subset {\bf \bar{126}}$ and $({\bf \bar{10},1,3}) (\equiv {\bf \Delta}_R) \subset {\bf 126}$ multiplets of ${\rm SU}(4) \times {\rm SU}(2)_L \times {\rm SU}(2)_R \subset {\rm SO}(10)$ becomes a physical degree of freedom identified with the axion. Then, the PQ symmetry breaking scale ($\Lambda_{\rm PQ}$) and the $B-L$ symmetry breaking scale ($\Lambda_{\rm B-L}$) coincide through the VEV of ${\bf \bar{\Delta}}_R$. The scalar partner of the lightest right-handed neutrino is regarded as the inflaton, which gives a consistent density fluctuation for the CMB.Comment: 8 pages, no figure; the version to appear in JHE

Solving problems of 4D minimal SO(10) model in a warped extra dimension

The minimal renormalizable supersymmetric SO(10) model, an SO(10) framework with only one 10 and one 126 Higgs multiplets in the Yukawa sector, is attractive because of its high predictive power for the neutrino oscillation data. However, this model suffers from problems related to running of gauge couplings. The gauge coupling unification may be spoiled due to the presence of Higgs multiplets much lighter than the grand unification (GUT) scale. In addition, the gauge couplings blow up around the GUT scale because of the presence of Higgs multiplets of large representations. We consider the minimal SO(10) model in the warped extra dimension and find a possibility to solve these problems.Comment: 12 pages, no figure; version to appear in Phys. Rev.

A simple SO(10) GUT in five dimensions

A simple supersymmetric SO(10) GUT in five dimensions is considered. The fifth dimension is compactified on the $S^1/(Z_2\times Z_2^\prime)$ orbifold possessing two inequivalent fixed points. In our setup, all matter and Higgs multiplets reside on one brane (PS brane) where the original SO(10) gauge group is broken down to the Pati-Salam (PS) gauge group, SU(4)_c \timesSU(2)_L \times SU(2)$_R$, by the orbifold boundary condition, while only the SO(10) gauge multiplet resides in the bulk. The further breaking of the PS symmetry to the Standard Model gauge group is realized by Higgs multiplets on the PS brane as usual in four dimensional models. Proton decay is fully suppressed. In our simple setup, the gauge coupling unification is realized after incorporating threshold corrections of Kaluza-Klein modes. When supersymmetry is assumed to be broken on the other brane, supersymmetry breaking is transmitted to the PS brane through the gaugino mediation with the bulk gauge multiplet.Comment: 12 pages, 1 figure, some errors have been corrected (no change in conclusions

General considerations of matter coupling with the self-dual connection

It has been shown for low-spin fields that the use of only the self-dual part of the connection as basic variable does not lead to extra conditions or inconsistencies. We study whether this is true for more general chiral action. We generalize the chiral gravitational action, and assume that half-integer spin fields are coupled with torsion linearly. The equation for torsion is solved and substituted back into the generalized chiral action, giving four-fermion contact terms. If these contact terms are complex, the imaginary part will give rise to extra conditions for the gravitational and matter field equations. We study the four-fermion contact terms taking spin-1/2 and spin-3/2 fields as examples.Comment: 16 pages, late