Stability analysis of inflation with an SU(2) gauge field

We study anisotropic cosmologies of a scalar field interacting with an SU(2) gauge field via a gauge-kinetic coupling. We analyze Bianchi class A models, which include Bianchi type I, II, VI0, VII0, VIII and IX. The linear stability of isotropic inflationary solution with background magnetic field is shown, which generalizes the known results for U(1) gauge fields. We also study anisotropic inflationary solutions, all of which turn out to be unstable. Then nonlinear stability for the isotropic inflationary solution is examined by numerically investigating the dependence of the late-time behaviour on the initial conditions. We present a number of novel features that may well affect physical predictions and viability of the models. First, in the absence of spatial curvature, strong initial anisotropy leads to a rapid oscillation of gauge field, thwarting convergence to the inflationary attractor. Secondly, the inclusion of spatial curvature destabilizes the oscillatory attractor and the global stability of the isotropic inflation with gauge field is restored. Finally, based on the numerical evidence combined with the knowledge of the eigenvalues for various inflationary solutions, we give a generic lower-bound for the duration of transient anisotropic inflation, which is inversely proportional to the slow-roll parameter.Comment: Published versio

Quantum Kinetics of Deconfinement Transitions in Dense Nuclear Matter: Dissipation Effects at Low Temperatures

Effects of energy dissipation on quantum nucleation of two-flavor quark matter in dense nuclear matter encountered in neutron star cores are examined at low temperatures. We find that low-energy excitations of nucleons and electrons reduce the nucleation rate exponentially via their collisions with the surface of a quark matter droplet.Comment: 9 pages (LaTeX, PTP style), 2 Postscript figures, to be published in Prog. Theor. Phys. (Letters

A note for Gromov's distance functions on the space of mm-spaces

This is just a note for \cite[Chapter$3{1/2}_+$]{gromov}. Maybe this note is obvious for a reader who knows metric geometry. I wish that someone study further in this direction.Comment: 21page

Doubly-charged Higgs bosons in the diboson decay scenario at the ILC

The Higgs Triplet Model (HTM) is one of important examples for extended Higgs sectors, because tiny neutrino masses can be simply explained. Unlike the canonical type-I seesaw model, a scale of new particles can be taken as $\mathcal{O}(100)$ GeV keeping an enough amount of production cross section for direct searches at collider experiments. In the HTM, there appear doubly-charged Higgs bosons $H^{\pm\pm}$, and detection of them is a key to probe the model. The decay property of $H^{\pm\pm}$ depends on the magnitude of the vacuum expectation value of the triplet field $v_\Delta$. When $v_\Delta$ is smaller than about 1 MeV, $H^{\pm\pm}$ can mainly decay into the same-sign dilepton, and the lower mass limit for $H^{\pm\pm}$ had been taken to be about 400 GeV at the LHC. On the other hand, if $v_\Delta$ is larger than about 1 MeV, $H^{\pm\pm}$ can mainly decay into the same-sign diboson. In this case, the mass bound cannot be applied, so that the scenario based on light $H^{\pm\pm}$ is still possible. In this talk, we discuss the phenomenology of the same-sign diboson decay scenario of $H^{\pm\pm}$. First, we review the mass bound from the current collider experiments given in Ref. \cite{KYY}. We then discuss the strategy for detection of $H^{\pm\pm}$ at the ILC.Comment: Talk presented at the International Workshop on Future Linear Colliders (LCWS13), Tokyo, Japan, 11-15 November 2013. References are adde

Grove-Shiohama type sphere theorem in Finsler geometry

From radial curvature geometry's standpoint, we prove a sphere theorem of the Grove-Shiohama type for a certain class of compact Finsler manifolds.Comment: The version 3 was corrected as follows: L_m (c) < \pi replaced with L_m (c) \leq rad_p in the (3) of Theorem 1.3. And some other minor changes have been done in the version 4. 16 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1210.177

Higgs boson couplings as a probe of new physics

Precise measurements of various coupling constants of the 125 GeV Higgs boson $h$ are one of the most important and solid methods to determine the structure of the Higgs sector. If we find deviations in the $h$ coupling constants from the standard model predictions, it can be an indirect evidence of the existence of additional Higgs bosons in non-minimal Higgs sectors. Furthermore, we can distinguish non-minimal Higgs sectors by measuring a pattern of deviations in various $h$ couplings. In this talk, we show patterns of the deviations in several simple non-minimal Higgs sectors, especially for the gauge $hVV$ and Yukawa $hf\bar{f}$ couplings. This talk is based on the paper [1].Comment: prepared for Proceedings of the HPNP2015 Conferenc

Embedding proper ultrametric spaces into ℓp\ell_p and its application to nonlinear Dvoretzky's theorem

We prove that every proper ultrametric space isometrically embeds into $\ell_p$ for any $p\geq 1$. As an application we discuss an $\ell_p$-version of nonlinear Dvoretzky's theorem.Comment: 6 page

Essential commutants of semicrossed products

Let $\alpha:G \curvearrowright M$ be a spatial action of countable abelian group on a "spatial" von Neumann algebra $M$ and $S$ be its unital subsemigroup with $G=S^{-1}S$. We explicitly compute the essential commutant and the essential fixed-points, modulo the Schatten $p$-class or the compact operators, of the w$^*$-semicrossed product of $M$ by $S$ when $M'$ contains no non-zero compact operators. We also prove a weaker result when $M$ is a von Neumann algebra on a finite dimensional Hilbert space and $(G,S)=(\mathbb{Z},\mathbb{Z}_{+})$, which extends a famous result due to Davidson (1977) for the classical analytic Toeplitz operators.Comment: 13 page

Observable concentration of mm-spaces into nonpositively curved manifolds

The measure concentration property of an mm-space $X$ is roughly described as that any 1-Lipschitz map on $X$ to a metric space $Y$ is almost close to a constant map. The target space $Y$ is called the screen. The case of $Y=\mathbb{R}$ is widely studied in many literature (see \cite{gromov}, \cite{ledoux}, \cite{mil2}, \cite{milsch}, \cite{sch}, \cite{tal}, \cite{tal2} and its reference). M. Gromov developed the theory of measure concentration in the case where the screen $Y$ is not necessarily $\mathbb{R}$ (cf. \cite{gromovcat}, {gromov2}, \cite{gromov}). In this paper, we consider the case where the screen $Y$ is a nonpositively curved manifolds. We also show that if the screen $Y$ is so big, then the mm-space $X$ does not concentrate.Comment: 31 pages,1 figur

Estimates of Gromov's box distance

In 1999, M. Gromov introduced the box distance function \sikaku on the space of all mm-spaces. In this paper, by using the method of T. H. Colding (cf. \cite[Lemma 5.10]{Colding}), we estimate \sikaku(\mathbb{S}^n,\mathbb{S}^m) and \sikaku (\mathbb{C}P^n, \mathbb{C}P^m), where $\mathbb{S}^n$ is the $n$-dimensional unit sphere in $\mathbb{R}^{n+1}$ and $\mathbb{C}P^n$ is the $n$-dimensional complex projective space equipped with the Fubini-Study metric. In paticular, we give the complete answer to an Exercise of Gromov's Green book (cf. \cite[Section $3{1/2}.18$]{gromov}). We also estimate \sikaku \big(SO(n), SO(m)\big) from below, where SO(n) is the special orthogonal group.Comment: 11page