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

Bubble Universes With Different Gravitational Constants

We argue a scenario motivated by the context of string landscape, where our universe is produced by a new vacuum bubble embedded in an old bubble and these bubble universes have not only different cosmological constants, but also their own different gravitational constants. We study these effects on the primordial curvature perturbations. In order to construct a model of varying gravitational constants, we use the Jordan-Brans-Dicke (JBD) theory where different expectation values of scalar fields produce difference of constants. In this system, we investigate the nucleation of bubble universe and dynamics of the wall separating two spacetimes. In particular, the primordial curvature perturbation on superhorizon scales can be affected by the wall trajectory as the boundary effect. We show the effect of gravitational constant in the exterior bubble universe can provide a peak like a bump feature at a large scale in a modulation of power spectrum.Comment: 15 pages, 6 figure

Dynamical angled brane

We discuss the dynamical D$p$-brane solutions describing any number of D$p$-branes whose relative orientations are given by certain SU(2) rotations. These are the generalization of the static angled D$p$-brane solutions. We study the collision of dynamical D3-brane with angles in type II string theory, and show that the particular orientation of the smeared D3-brane configuration can provide an example of colliding branes if they have the same charges. Otherwise a singularity appears before D3-branes collide.Comment: 25 pages, 7 figure

Chaos in Schwarzschild Spacetime : The Motion of a Spinning Particle

We study the motion of a spinning test particle in Schwarzschild spacetime, analyzing the Poincar\'e map and the Lyapunov exponent. We find chaotic behavior for a particle with spin higher than some critical value (e.g. $S_{cr} \sim 0.64 \mu M$ for the total angular momentum $J=4 \mu M$), where $\mu$ and $M$ are the masses of a particle and of a black hole, respectively. The inverse of the Lyapunov exponent in the most chaotic case is about three orbital periods, which suggests that chaos of a spinning particle may become important in some relativistic astrophysical phenomena. The ``effective potential" analysis enables us to classify the particle orbits into four types as follows. When the total angular momentum $J$ is large, some orbits are bounded and the ``effective potential"s are classified into two types: (B1) one saddle point (unstable circular orbit) and one minimal point (stable circular orbit) on the equatorial plane exist for small spin; and (B2) two saddle points bifurcate from the equatorial plane and one minimal point remains on the equatorial plane for large spin. When $J$ is small, no bound orbits exist and the potentials are classified into another two types: (U1) no extremal point is found for small spin; and (U2) one saddle point appears on the equatorial plane, which is unstable in the direction perpendicular to the equatorial plane, for large spin. The types (B1) and (U1) are the same as those for a spinless particle, but the potentials (B2) and (U2) are new types caused by spin-orbit coupling. The chaotic behavior is found only in the type (B2) potential. The ``heteroclinic orbit'', which could cause chaos, is also observed in type (B2).Comment: 18 pages, revtex, 9 figures(figures are available on request

Covariant Gravitational Equations on Brane World with Gauss-Bonnet term

We present the covariant gravitational equations to describe a four-dimensional brane world in the case with the Gauss-Bonnet term in a bulk spacetime, assuming that gravity is confined on the $Z_2$ symmetric brane. It contains some components of five-dimensional Weyl curvature ($E_{\mu\nu}$) which describes all effects from the bulk spacetime just as in the case of the Randall-Sundrum second model. Applying this formalism to cosmology, we derive the generalized Friedmann equation and calculate the Weyl curvature term, which is directly obtained from a black hole solution.Comment: 14 pages, no figur

Cosmology in ghost-free bigravity theory with twin matter fluids: The origin of "dark matter"

We study dynamics of Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime based on the ghost-free bigravity theory. Assuming the coupling parameters guaranteeing the existence of de Sitter space as well as Minkowski spacetime, we find two stable attractors for spacetime with "twin" dust matter fields: One is de Sitter accelerating universe and the other is matter dominated universe. Although a considerable number of initial data leads to de Sitter universe, we also find matter dominated universe or spacetime with a future singularity for some initial data. The cosmic no-hair conjecture does not exactly hold, but the accelerating expansion can be found naturally. The $\Lambda$-CDM model is obtained as an attractor. We also show that the dark matter component in the Friedmann equation, which originates from another twin matter, can be about 5 times larger than the baryonic matter, by choosing the appropriate coupling constants.Comment: 23 pages, 24 figure

Black Hole in the Expanding Universe with Arbitrary Power-Law Expansion

We present a time-dependent and spatially inhomogeneous solution that interpolates the extremal Reissner-Nordstr\"om (RN) black hole and the Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe with arbitrary power-law expansion. It is an exact solution of the $D$-dimensional Einstein-"Maxwell"-dilaton system, where two Abelian gauge fields couple to the dilaton with different coupling constants, and the dilaton field has a Liouville-type exponential potential. It is shown that the system satisfies the weak energy condition. The solution involves two harmonic functions on a $(D-1)$-dimensional Ricci-flat base space. In the case where the harmonics have a single-point source on the Euclidean space, we find that the spacetime describes a spherically symmetric charged black hole in the FLRW universe, which is characterized by three parameters: the steepness parameter of the dilaton potential $n_T$, the U$(1)$ charge $Q$, and the "nonextremality" $\tau$. In contrast with the extremal RN solution, the spacetime admits a nondegenerate Killing horizon unless these parameters are finely tuned. The global spacetime structures are discussed in detail.Comment: 22 pages, 8 figures, 1 table; v2: typos corrected, references added, version to appear in PR

Dynamical brane with angles : Collision of the universes

We present the time-dependent solutions corresponding to the dynamical D-brane with angles in ten-dimensional type II supergravity theories. Our solutions with angles are different from the known dynamical intersecting brane solutions in supergravity theories. Because of our ansatz for fields, all warp factors in the solutions can depend on time. Applying these solutions, we construct cosmological models from those solutions by smearing some dimensions and compactifying the internal space. We find the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological solutions with power-law expansion. We also discuss the dynamics of branes based on these solutions. When the spacetime is contracting in ten dimensions, each brane approaches the others as the time evolves. However, for Dp-brane ($p\le 7$) without smearing branes, a singularity appears before branes collide. In contrast, the D6-D8 brane system or the smeared D(p-2)-Dp brane system with one uncompactified extra dimension can provide an example of colliding branes (and collision of the universes), if they have the same charges.Comment: 34 pages, 8 figure

Dark matter in ghost-free bigravity theory: From a galaxy scale to the universe

We study the origin of dark matter based on the ghost-free bigravity theory with twin matter fluids. The present cosmic acceleration can be explained by the existence of graviton mass, while dark matter is required in several cosmological situations [the galactic missing mass, the cosmic structure formation and the standard big-bang scenario (the cosmological nucleosynthesis vs the CMB observation)]. Assuming that the Compton wavelength of the massive graviton is shorter than a galactic scale, we show the bigravity theory can explain dark matter by twin matter fluid as well as the cosmic acceleration by tuning appropriate coupling constants.Comment: 15 pages, 7 figures, minor changes, references adde

Condensate of Massive Graviton and Dark Matter

We study coherently oscillating massive gravitons in the ghost-free bigravity theory. This coherent field can be interpreted as a condensate of the massive gravitons. We first define the effective energy-momentum tensor of the coherent massive gravitons in a curved spacetime. We then study the background dynamics of the universe and the cosmic structure formation including the effects of the coherent massive gravitons. We find that the condensate of the massive graviton behaves as a dark matter component of the universe. From the geometrical point of view the condensate is regarded as a spacetime anisotropy. Hence, in our scenario, dark matter is originated from the tiny deformation of the spacetime. We also discuss a production of the spacetime anisotropy and find that the extragalactic magnetic field of a primordial origin can yield a sufficient amount for dark matter.Comment: 25 pages, 3 figures; v2: minor improvements, references added, published versio