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Recently, in Gong {\em et al} \cite{GWW07} and Wang and Santos \cite{WS07} itwas shown that the effective cosmological constant on each of the two orbifoldbranes can be easily lowered to its current observational value, by using thelarge extra dimensions in the framework of both M-Theory and string theory on$S^{1}/Z_{2}$. In this paper, we study the current acceleration of theuniverse, using the formulas developed in \cite{WS07}. We first constructexplicitly time-dependent solution to the 10-dimensional bulk of theNeveu-Schwarz/Neveu-Schwarz sector, compactified on a 5-dimensional torus.Then, we write down the generalized Friedmann equations on each of the twodynamical branes, and fit the models to the 182 gold supernova Ia data and theBAO parameter from SDSS, using both of our MINUIT and Monte-Carlo Markov Chain(MCMC) codes. With the best fitting values of the parameters involved asinitial conditions, we integrate the generalized Friedmann equationsnumerically and find the future evolution of the universe. We find that itdepends on the choice of the radion potentials $V_{4}^{(I)} (I = 1, 2)$ of thebranes. In particular, when choosing them to be the Goldberger-Wise potentials,$V_{4}^{(I)} = \lambda_{4}^{(I)} (\psi^{2} - {v_{I}}^{2})^{2}$, we find thatthe current acceleration of the universe driven by the effective cosmologicalconstant is only temporary. Due to the effects of the potentials, the universewill be finally in its decelerating expansion phase again. We also study theproper distance between the two branes, and find that it remains almostconstant during the whole future evolution of the universe in all the modelsconsidered.

Late transient acceleration of the universe in string theory on $S^{1}/Z_{2}$