Geometry and cosmological perturbations in the bulk inflaton model

We consider a braneworld inflation model driven by the dynamics of a scalar field living in the 5-dimensional bulk, the so-called 'bulk inflaton model', and investigate the geometry in the bulk and large scale cosmological perturbations on the brane. The bulk gravitational effects on the brane are described by a projection of the 5-dimensional Weyl tensor, which we denote by Eμν. Focusing on a tachyonic potential model, we take a perturbative approach in the anti-de Sitter (AdS5) background with a single de Sitter brane. We first formulate the evolution equations for Eμν in the bulk. Next, applying them to the case of a spatially homogeneous brane, we obtain two different integral expressions for Eμν. One of them reduces to the expression obtained previously when evaluated on the brane. The other is a new expression that may be useful for analyzing the bulk geometry. Then we consider superhorizon scale cosmological perturbations and evaluate the bulk effects onto the brane. In the limit H2l2<<1, where H is the Hubble parameter on the brane and l is the bulk curvature radius, we find that the effective theory on the brane is identical to the 4-dimensional Einstein-scalar theory with a simple rescaling of the potential even under the presence of inhomogeneities. In particular, it is found that the anticipated nontrivial bulk effect due to the spatially anisotropic part of Eμν may appear only at O(H4l4)