Cosmological constant of the inflating branes in the Randall-Sundrum-Oda model

We examine the issue of the cosmological constant in the many inflating bra nes scenario, extending on two recent models by I. Oda and Randall-Sundrum. The exact solution in a closed form is found in the slow-roll approximatio n for the branes. We show that each positive tension brane has an induced c anonical cosmological constant and expansion rate that axe decreasing funct ions of their position in the fifth dimension. The reason is that the square of the effective expansion rate enters as a s ource term in the Einstein equations for the branes. Thus the brans has two scale factors depending on time and the fifth dimension respectively. A di splacement of the brane along the fifth dimension would adjust its effectiv e expansion rate in such a way that it compensates for its internal energy changes due to inflation and possible phase transitions.