Initial Kaluza-Klein fluctuations and inflationary gravitational waves in braneworld cosmology

We study the spectrum of gravitational waves generated from inflation in the Randall-Sundrum braneworld. Since the inflationary gravitational waves are of quantum-mechanical origin, the initial configuration of perturbations in the bulk includes Kaluza-Klein quantum fluctuations as well as fluctuations in the zero mode. We show, however, that the initial fluctuations in Kaluza-Klein modes have no significant effect on the late time spectrum, irrespective of the energy scale of inflation and the equation of state parameter in the post-inflationary stage. This is done numerically, using the Wronskian formulation.Comment: 7 pages, 6 figure

Formation of \eta'(958)-mesic nuclei and axial U_A(1) anomaly at finite density

We discuss the possibility to produce the bound states of the $\eta'(958)$ meson in nuclei theoretically. We calculate the formation cross sections of the $\eta'$ bound states with the Green function method for ($\gamma$,p) reaction and discuss the experimental feasibility at photon facilities like SPring-8. We conclude that we can expect to observe resonance peaks in ($\gamma$,p) spectra for the formation of $\eta'$ bound states and we can deduce new information on $\eta'$ properties at finite density. These observations are believed to be essential to know the possible mass shift of $\eta'$ and deduce new information of the effective restoration of the chiral $U_A(1)$ anomaly in the nuclear medium.Comment: 4 pages, 3 figure

Restrictions of generalized Verma modules to symmetric pairs

We initiate a new line of investigation on branching problems for generalized Verma modules with respect to complex reductive symmetric pairs (g,k). Here we note that Verma modules of g may not contain any simple module when restricted to a reductive subalgebra k in general. In this article, using the geometry of K_C orbits on the generalized flag variety G_C/P_C, we give a necessary and sufficient condition on the triple (g,k, p) such that the restriction X|_k always contains simple k-modules for any g-module $X$ lying in the parabolic BGG category O^p attached to a parabolic subalgebra p of g. Formulas are derived for the Gelfand-Kirillov dimension of any simple k-module occurring in a simple generalized Verma module of g. We then prove that the restriction X|_k is multiplicity-free for any generic g-module X \in O if and only if (g,k) is isomorphic to a direct sum of (A_n,A_{n-1}), (B_n,D_n), or (D_{n+1},B_n). We also see that the restriction X|_k is multiplicity-free for any symmetric pair (g, k) and any parabolic subalgebra p with abelian nilradical and for any generic g-module X \in O^p. Explicit branching laws are also presented.Comment: 31 pages, To appear in Transformation Group

The spectrum of gravitational waves in Randall-Sundrum braneworld cosmology

We study the generation and evolution of gravitational waves (tensor perturbations) in the context of Randall-Sundrum braneworld cosmology. We assume that the initial and final stages of the background cosmological model are given by de Sitter and Minkowski phases, respectively, and they are connected smoothly by a radiation-dominated phase. This setup allows us to discuss the quantum-mechanical generation of the perturbations and to see the final amplitude of the well-defined zero mode. Using the Wronskian formulation, we numerically compute the power spectrum of gravitational waves, and find that the effect of initial vacuum fluctuations in the Kaluza-Klein modes is subdominant, contributing not more than 10% of the total power spectrum. Thus it is confirmed that the damping due to the Kaluza-Klein mode generation and the enhancement due to the modification of the background Friedmann equation are the two dominant effects, but they cancel each other, leading to the same spectral tilt as the standard four-dimensional result. Kaluza-Klein gravitons that escape from the brane contribute to the energy density of the dark radiation at late times. We show that a tiny amount of the dark radiation is generated due to this process.Comment: 10 pages, 5 figures; v2: published versio

Global analysis by hidden symmetry

Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects: (A) global analysis on X by using representations of G (hidden symmetry); (B) global analysis on X by using representations of G'; (C) branching laws of representations of G when restricted to the subgroup G'. We explain a trick which transfers results for finite-dimensional representations in the compact setting to those for infinite-dimensional representations in the noncompact setting when $X_C$ is $G_C$-spherical. Applications to branching problems of unitary representations, and to spectral analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th birthda

Implementation of Lees-Edwards periodic boundary conditions for direct numerical simulations of particle dispersions under shear flow

A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees-Edwards periodic boundary conditions. The Navier-Stokes equation is solved in oblique coordinates to resolve the incompatibility of the fluid motions with the sheared geometry, and the force coupling between colloidal particles and the host fluid is imposed by using a smoothed profile method. The validity of the method is carefully examined by comparing the present numerical results with experimental viscosity data for particle dispersions in a wide range of volume fractions and shear rates including nonlinear shear-thinning regimes

Low energy effective theory on a regularized brane in six-dimensional flux compactifications

Conical brane singularities in six-dimensional flux compactification models can be resolved by introducing cylindrical codimension-one branes with regular caps instead of 3-branes (a la Kaluza-Klein braneworlds with fluxes). In this paper, we consider such a regularized braneworld with axial symmetry in six-dimensional Einstein-Maxwell theory. We derive a low energy effective theory on the regularized brane by employing the gradient expansion approach, and show that standard four-dimensional Einstein gravity is recovered at low energies. Our effective equations extend to the nonlinear gravity regime, implying that conventional cosmology can be reproduced in the regularized braneworld.Comment: 11 pages, minor corrections, accepted for publication in Physical Review

Universal charge transport of the Mn oxides in the high temperature limit

We have found that various Mn oxides have the universal resistivity and thermopower in the high temperature limit. The resistivities and thermopowers of all the samples go toward constant values of 7$\pm$1 m$\Omega$cm and $-79\pm$3 $\mu$V/K, which are independent of carrier density and crystal structures. We propose that the electric conduction occurs in a highly localized way in the high temperature limit, where the exchange of entropy and charge occurs in the neighboring Mn$^{3+}$ and Mn$^{4+}$ ions.Comment: 4 pages, 4 eps figures, to be published in J. Appl. Phy