Hideo Kodama

Brane world cosmology: Gauge-invariant formalism for perturbation

In the present paper the gauge-invariant formalism is developed for perturbations of the brane-world model in which our universe is realized as a boundary of a higher-dimensional spacetime. For the background model in which the bulk spacetime is

Conserved Energy Flux for the Spherically Symmetric System and the Backreaction Problem in the Black Hole Evaporation

(n+m)

Specialization of Ashtekar's Formalism to Bianchi Cosmology

-dimensional and has the spatial symmetry corresponding to the isometry group of a

Multi-production of universes by first-order phase transition of a vacuum

n

Abundance of Primordial Holes Produced by Cosmological First-Order Phase Transition

-dimensional maximally symmetric space, gauge-invariant equations are derived for perturbations of the bulk spacetime. Further for the case corresponding to the brane-world model in which

Creation of Schwarzschild-de Sitter wormholes by a cosmological first-order phase transition

m=2

EVOLUTION OF ISOCURVATURE PERTURBATIONS I: PHOTON-BARYON UNIVERSE

and the brane is a boundary invariant under the spatial symmetry in the unperturbed background, relations between the gauge-invariant variables describing the bulk perturbations and those for brane perturbations are derived from Israels junction condition under the assumption of

Global structure of the Zipoy–Voorhees–Weyl spacetime and the δ = 2 Tomimatsu–Sato spacetime

ZR_2

The isotropy of compact universes

symmetry. In particular, for the case in which the bulk spacetime is a constant-curvature spacetime, it is shown that the bulk perturbation equations reduce to a single hyperbolic master equation for a master variable, and that the physical condition on the gauge-invariant variable describing the intrinsic stress perturbation of the brane yield a boundary condition for the master equation through the junction condition. On the basis of this formalism it is pointed out that it seems to be difficult to suppress brane perturbations corresponding to massive excitations for a brane motion giving a realistic expanding universe model.

ALL UNIVERSES GREAT AND SMALL

For the spherically symmetric system, we prove the existence o{ a new locally cotEen·ecl flux which can be interpreted to represent the total energy flux of matter and gravitational field. ·with the aid of this conservation law, we study the relation between the behavior of the event horizon and the energy flux across it and look for constraints imposed on the total energy radiated to infinity. Some implications of the results of this study to the backreaction problem in the black hole evaporation are discussed.