name{{sgn}}(c) \frac{(k_{1}^{2} - k_{2}^{2}) b^{2}}{2 \G(a)} 
\g\left(3a, \left\lvert \frac{c}{b} \right\rvert^{\frac{1}{a}} \right). \nonumber\end{aligned}$$

Naoya Yamaguchi\
Office for Establishment of an Information-related School\
Nagasaki University\
1-14 Bunkyo, Nagasaki City 852-8521\
Japan\
yamaguchi@nagasaki-u.ac.jp

Yuka Yamaguchi\
Office for Establishment of an Information-related School\
Nagasaki University\
1-14 Bunkyo, Nagasaki City 852-8521\
Japan\
yamaguchiyuka@nagasaki-u.ac.jp

Ryuei Nishi\
Office for Establishment of an Information-related School\
Nagasaki University\
1-14 Bunkyo, Nagasaki City 852-8521\
Japan\
nishii.ryuei@nagasaki-u.ac.jp


---
abstract: |
    We examine the issue of the cosmological constant in the $many$ $inflating$ branes 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 approximation of the radion. Defining an effective expansion rate, which depends on the location of each brane in the fifth dimension and demanding stability for this case we show that each positive tension brane has a localized, decaying cosmological constant (the opposite process applies to the negative energy branes \[4\]) .\
    The reason is that the square of the effective expansion rate enters as a source term in the Einstein equations for the branes.Thus the brane has two scale factors depending on time and the fifth dimnesion respectively .The brane will roll along the fifth dimension in order to readjust its effective expansion rate in such a way that it compensates for its internal energy changes due to inflation and possible phase transitions.
author:
- |
    Laura Mersini\
    Department of Physics\
    University of Wisconsin-Milwaukee\
    Milwaukee, WI 53201\
    lmersini@uwm.edu\
    Wisc-Milw-99Th-14
date: 'September 20, 1999'
title: 'Decaying Cosmological Constant of the Inflating Branes in the Randall-Sundrum -Oda Model'
---

Setup
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In this paper we consider and find solutions to a five dimensional m