Brane world cosmology: Gauge invariant formalism for perturbation

By H. Kodama, A. Ishibashi, O. Seto. 2000

230 citations recorded by the source corpus.

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 $(n+m)$-dimensional and has the spatial symmetry corresponding to the isometry group of a $n$-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 $m=2$ 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 Israel's junction condition under the assumption of $\ZR_2$ 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8e598e538d4ad9048c8201ccb9e1f3b602c66673

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Citations in the corpus

Modified Gravity and Cosmology (2011, methodology): “We should now view these equations as follows [716]: Equations (725) and (726) fix δ̂”
Static response and Love numbers of Schwarzschild black holes (2020, methodology): “In the higher-dimensional cases this was previously done at the equation of motion level: for the spin-1 case in [58–60] and for the spin-2 case in [61–63].”
Comparison between various notions of conserved charges in asymptotically AdS spacetimes (2005, background): “Some properties of these tensor harmonics and decomposition theorems are given in [43, 61 ].”
Brane-World Gravity (2004, background): “The theory of gauge-invariant perturbations in brane-world cosmology has been extensively investigated and developed [303, 271, 24, 308, 99, 312, 369, 346, 286, 177, 272, 176, 331, 333, 190, 235, 265, 416, 258, 332, 417, 231, 266, 191, 123, 158, 234, 50, 127, 340, 385, 368, 285, 85, 90, 116, 41, 54,”
The global non-linear stability of the Kerr-de Sitter family of black holes (2016, methodology): “These works rely on a decomposition of tensors into scalar and vector parts, as discussed in [93]; we restrict our discussion here to the case of interest in the present paper, namely we work in three spatial dimensions, so the spherical metric is the round metric on S(2), corresponding to taking n=”
Wilsonian approach to fluid/gravity duality (2010, background): “One important feature, demonstrated in [17] and [13], is that the linearized gravity fluctuations decouple into so-called vector, scalar (or sound) and tensor type, characterized by their transformations under the O(p) rotational symmetry.”