  We introduce the brane-bulk interaction to discuss a limitation of the
cosmological Cardy-Verlinde formula which is useful for the holographic
description of brane cosmology. In the presence of the brane-bulk interaction,
we cannot find the entropy representation of the first Friedmann equation (the
cosmological Cardy-Verlinde formula). In the absence of the interaction, the
cosmological Cardy-Verlinde formula is established even for the time-dependent
charged AdS background. Hence, if there exists a dynamic exchange of energy
between the brane and the bulk (that is, if $\tilde T^t~_y \not=0$), we cannot
achieve the cosmological holographic principle on the brane.
