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 m = −2(2l− 1)(l+ 1)H and m = −2l(2l+ 3)H where l is an integer. There are two branches (± branches) of solutions for the background spacetime. In the + branch, which includes the selfaccelerating universe, a resonance appears for a mode with m = 2H due to a spin-0 perturbation with m = 2H. The self-accelerating universe has a distinct feature because there is also a helicity0 mode of spin-2 perturbations with m = 2H. 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 van Dam-Veltman-Zakharov discontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that the lineariaed gravity on the brane is well described by the Brans-Dicke theory with ω = 3Hrc in − branch and ω = −3Hrc in + branch, respectively, which confirms the existence of the ghost in + branch. We also study large scale perturbations. In + branch, the resonance induces a non-trivial anisotropic stress on the brane via the projection of Weyl tensor in the bulk, but no instability is shown to exist on the brane.