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Ryo Takahashi

Publications and source records attributed to Ryo Takahashi.

233 records · Page 13Linked to original sources
arXiv2007

False Vacuum in the Supersymmetric Mass Varying Neutrinos Model

We present detailed analyses of the vacuum structure of the scalar potential in a supersymmetric Mass Varying Neutrinos model. The observed dark energy density is identified with false vacuum energy and the dark energy scale of order $(10^{-3}eV)^4$ is understood by gravitationally suppressed supersymmetry breaking scale, $F({TeV})^2/M_{Pl}$, in the model. The vacuum expectation values of sneutrinos should be tiny in order that the model works. Some decay processes of superparticles into acceleron and sterile neutrino are also discussed in the model.

hep-ph↗
arXiv2007

Quasi-socle ideals in a Gorenstein local ring

This paper explores the structure of quasi-socle ideals I=Q:m^2 in a Gorenstein local ring A, where Q is a parameter ideal and m is the maximal ideal in A. The purpose is to answer the problem of when Q is a reduction of I and when the associated graded ring G(I) = \bigoplus_{n \geq 0}I^n/I^{n+1} is Cohen-Macaulay. Wild examples are explored.

math.AC↗
arXiv2007

Dark energy and neutrino model in SUSY -- Remarks on active and sterile neutrinos mixing --

We consider a Mass Varying Neutrinos (MaVaNs) model in supersymmetric theory. The model includes effects of supersymmetry breaking transmitted by the gravitational interaction from the hidden sector, in which supersymmetry was broken, to the dark energy sector. Then evolutions of the neutrino mass and the equation of state parameter of the dark energy 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.

hep-ph↗
arXiv2007

Direct summands of syzygy modules of the residue class field

Let R be a commutative Noetherian local ring. This paper deals with the problem asking whether R is Gorenstein if the n-th syzygy of the residue field of R has a nontrivial direct summand of finite G-dimension for some n. It is proved that if n is at most two then it is true, and moreover, the structure of the ring R is determined essentially uniquely.

math.AC↗
arXiv2006

Dark Energy and Neutrino Model in SUSY

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.

hep-ph↗
arXiv2006

An uncountably infinite number of indecomposable totally reflexive modules

A few years ago, Huneke and Leuschke proved a theorem which solved a conjecture of Schreyer. It asserts that an excellent Cohen-Macaulay local ring of countable Cohen-Macaulay type which is complete or has uncountable residue field has at most a one-dimensional singular locus. In this paper, it is verified that the assumption of the excellent property can be removed, and the theorem is considered over an arbitrary local ring. The main purpose of this paper is to prove that the existence of a certain prime ideal and a certain totally reflexive module implies the existence of an uncountably infinite number of isomorphism classes of indecomposable totally reflexive modules.

math.AC↗
arXiv2006

On the number of indecomposable totally reflexive modules

In this note, it is proved that over a commutative noetherian henselian non-Gorenstein local ring there are infinitely many isomorphism classes of indecomposable totally reflexive modules, if there is a nonfree cyclic totally reflexive module.

math.AC↗
arXiv2006

Speed of Sound in the Mass Varying Neutrinos Scenario

We discuss about the speed of sound squared in the Mass Varying Neutrinos scenario (MaVaNs). Recently, it was argued that the MaVaNs has a catastrophic instability which is the emergence of an imaginary speed of sound at the non-relativistic limit of neutrinos. As the result of this instability, the neutrino-acceleron fluid cannot act as the dark energy. However, it is found that the speed of sound squared in the neutrino-acceleron fluid could be positive in our model. We examine the speed of sound in two cases of the scalar potential. One is the small fractional power-law potential and another is the logarithmic one. The power-law potential model with the right-handed neutrinos gives a stable one.

astro-ph↗
arXiv2005

Embedding the Texture of the Neutrino Mass Matrix into the MaVaNs Scenario

We have embedded the texture of the neutrino mass matrix with three families into the MaVaNs scenario. We take the power-law potential of the acceleron field and a typical texture of active neutrinos, which is derived by the D_4 symmetry and predicts the maximal mixing of the atmospheric neutrino and the vanishing U_{e3}. The effect of couplings among the dark fermion and active neutrinos are studied by putting the current cosmological data and the terrestrial neutrino experimental data. It is found that the neutrino flavor mixings evolve as well as the neutrino masses. Especially, U_{e3} develops into the non-vanishing one and θ_{atm} deviates from the maximal mixing due to couplings among the dark fermion and active neutrinos.

hep-ph↗
arXiv2005

Model of Mass Varying Neutrinos in SUSY

We discuss the mass varying neutrino scenario in the supersymmetric theory. In the case of the model with the single superfield, one needs the soft SUSY breaking terms or the $μ$ term. However, fine-tunings of some parameters are required to be consistent with the cosmological data. In order to avoid the fine-tuning, we discuss the model with two superfields, which is consistent with the cosmological data. However, it is found that the left-handed neutrino mixes with the neutrino of the dark sector maximally. Adding a right- handed neutrino, which does not couple to the dark sector, we obtain a favorable model in the phenomenology of the neutrino experiments. In this model, the deceleration of the cosmological expansion converts to the acceleration near $z\simeq 0.5$. The speed of sound $c_s$ becomes imaginary if we put $ω_0=-0.9$, which corresponds to $m_ν^0=3.17\eV$. On the other hand, if we take $ω_0=-0.998$, which leads to $m_ν^0=0.05\eV$, $c_s^2$ becomes positive since $ω$ evolves rapidly near the present epoch in our model.

hep-ph↗
arXiv2005

Remarks on modules approximated by G-projective modules

Let $R$ be a commutative Noetherian Henselian local ring. Denote by $\mathrm{mod} R$ the category of finitely generated $R$-modules, and by ${\mathcal G}$ the full subcategory of $\mathrm{mod} R$ consisting of all G-projective $R$-modules. In this paper, we consider when a given $R$-module has a right ${\mathcal G}$-approximation. For this, we study the full subcategory $\mathrm{rap}{\mathcal G}$ of $\mathrm{mod} R$ consisting of all $R$-modules that admit right ${\mathcal G}$-approximations. We investigate the structure of $\mathrm{rap}{\mathcal G}$ by observing ${\mathcal G}$, ${\mathcal G}^{\bot}$ and $\mathrm{lap}{\mathcal G}$, where $\mathrm{lap}{\mathcal G}$ denotes the full subcategory of $\mathrm{mod} R$ consisting of all $R$-modules that admit left ${\mathcal G}$-approximations. On the other hand, we also characterize $\mathrm{rap}{\mathcal G}$ in terms of Tate cohomologies. We give several sufficient conditions for ${\mathcal G}$ to be contravariantly finite in $\mathrm{mod} R$.

math.AC↗
arXiv2005

Homological invariants associated to semi-dualizing bimodules

Cohen-Macaulay dimension for modules over a commutative noetherian local ring has been defined by A. A. Gerko. That is a homological invariant sharing many properties with projective dimension and Gorenstein dimension. The main purpose of this paper is to extend the notion of Cohen-Macaulay dimension for modules over commutative noetherian local rings to that for bounded complexes over non-commutative noetherian rings.

math.AC↗
arXiv2005

Syzygy modules with semidualizing or G-projective summands

Let R be a commutative Noetherian local ring with residue class field k. In this paper, we mainly investigate direct summands of the syzygy modules of k. We prove that R is regular if and only if some syzygy module of k has a semidualizing summand. After that, we consider whether R is Gorenstein if and only if some syzygy module of k has a G-projective summand.

math.AC↗