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 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 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.

我们在这里讨论了一个更高维的宇宙学模型，并解释了最近用 Chaplygin 类型的气体加速的现象。在这种情况下，可以减少额外空间的维度。我们的解决方案本质上是通用的，因为当\(d = 0\). 我们使用差异年龄方法获得的数据绘制了最佳拟合图，可以看出该图仅支持一个额外的维度。这意味着 Chaplygin 气体显然由 5D 世界主导。需要指出的是，这种情况下的最终方程本质上是高度非线性的。自然不可能随时间获得 4D 比例因子的显式解。为了避免这个困难，我们考虑了关键方程的一阶近似，这使得以精确形式获得 4D 比例因子的时间显式解以及额外维度的表达成为可能。可能需要指出的是，对于大的四维比例因子，此解决方案模仿\(\Lambda \)清洁发展机制模型。还对翻转时间的分析进行了一些详细的分析和图形研究。它清楚地表明早期翻转发生在更高维度上。还可以看出，对于更高的维度，降维的速度更快。所以我们可以得出结论，额外维度的紧化效应有助于加速。