We address the localization of gravity on the Friedmann-Robertson-Walker type brane embedded in either ${\mathrm{AdS}}_5$ or ${\mathrm{dS}}_5$ bulk space, and derive two definite limits between which the value of the bulk cosmological constant has to lie in order to localize the graviton on the brane. The lower limit implies that the brane should be either ${\mathrm{dS}}_4$ or 4D Minkowski in the ${\mathrm{AdS}}_5$ bulk. The positive upper limit indicates that the gravity can be trapped also on a curved brane in the ${\mathrm{dS}}_5$ bulk space. Some implications for recent cosmological scenarios are also discussed.

• Received 11 April 2002

DOI:https://doi.org/10.1103/PhysRevD.66.064016