  We investigate the effect of the bulk gravitational field on the cosmological
perturbations on a brane embedded in the 5D Anti-de Sitter (AdS) spacetime. The
effective 4D Einstein equations for the scalar cosmological perturbations on
the brane are obtained by solving the perturbations in the bulk. Then the
behaviour of the corrections induced by the bulk gravitational field to the
conventional 4D Einstein equation are determined. Two types of the corrections
are found. First we investigate the corrections which become significant at
scales below the AdS curvature scales and in the high energy universe with the
energy density larger than the tension of the brane. The evolution equation for
the perturbations on the brane is found and solved. Another type of the
corrections is induced on the brane if we consider the bulk perturbations which
do not contribute to the metric perturbations but do contribute to the matter
perturbations. At low energies, they have imaginary mass $m^2=-(2/3) \k^2$ in
the bulk where $\k$ is the 3D comoving wave number of the perturbations. They
diverge at the horizon of the AdS spacetime. The induced density perturbations
behave as sound waves with sound velocity $1/\sqrt{3}$ in the low energy
universe. At large scales, they are homogeneous perturbations that depend only
on time and decay like radiation. They can be identified as the perturbations
of the dark radiation. They produce isocurvature perturbations in the matter
dominated era. Their effects can be observed as the shifts of the location and
the height of the acoustic peak in the CMB spectrum.
