Gravity on de-Sitter 3-Brane, Induced Einstein-Hilbert Term and Massless Gravitons

We study the extensions of DGP model which are described by five-dimensional Einstein gravity coupled covariantly to 3-brane with induced gravity term and consider warped D=4 de Sitter background field solutions on the brane. The case with included D=5 AdS cosmological term is also considered. Following background field method we obtain the field equations described by the Lagrangean terms bilinear in gravitational field. In such a linear field approximation on curved dS background we calculate explicitly the five-dimensional massive terms as well as the mass-like ones on the brane. We investigate the eigenvalue problem of Schr\"{o}dinger-like equation in fifth dimension for graviton masses and discuss the existence of massless as well as massive graviton modes in the bulk and on the brane without and with induced gravity.