Inflaton perturbations in brane-world cosmology with induced gravity

We study cosmological perturbations in the brane models with an induced Einstein–Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza–Klein modes of bulk metric perturbations with mass and where is an integer. There are two branches (± branches) of solutions for the background spacetime. In the + branch, which includes the self-accelerating universe, a resonance appears for a mode with m2 = 2H2 due to a spin-0 perturbation with m2 = 2H2. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with m2 = 2H2. In the − branch, which can be thought as the Randall–Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related to the disappearance of the van Dam–Veltman–Zakharov discontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that the linearized gravity on the brane is well described by the Brans–Dicke theory with ω = 3Hrc in the − branch and ω = −3Hrc in the + branch, respectively, which confirms the existence of the ghost in the + branch. We also study large scale perturbations. In the + branch, the resonance induces a non-trivial anisotropic stress on the brane via the projection of the Weyl tensor in the bulk, but no instability is shown to exist on the brane