Accelerating Universe in Higher Dimensional Space Time : an alternative approach

We have discussed here a higher dimensional cosmological model and explained the recent acceleration with a Chaplygin type of gas. Dimensional reduction of extra space is possible in this case. Our solutions are general in nature because all the well known results of 4D Chaplygin driven cosmology are recovered when $d = 0$. We have drawn the best fit graph using the data obtained by the differential age method (CC) and it is seen that the graph favours only one extra dimension. That means the Chaplygin gas is apparently dominated by a 5D world. Relevant to point out that the final equation in this case are highly nonlinear in nature. Naturally it is not possible to obtain explicit solution of the 4D scale factor with time. To circumvent this difficulty, we consider a first order approximation of the key equation which has made it possible to get time explicit solution of 4D scale factor in exact form as well as the expression of extra dimensions. It may be pointed out that for large four dimensional scale factor this solution mimics $\Lambda$CDM model. An analysis of flip time is also studied both analytically and graphically in some detail. It clearly shows that early \emph{flip} occurs for higher dimensions. It is also seen that the rate of dimensional reduction is faster for higher dimensions. So we may conclude that the effect of compactification of extra dimension helps the acceleration.