Higher dimensional cosmological model with a time-dependent equation of state

A homogeneous cosmological model in higher dimension is obtained assuming a timedependent equation of state. It is observed that as usual 3-D space expands, extra space (space belonging to the other dimensions) reduces with time, thus exhibiting the desired feature of dimensional reduction. The dynamical behavior of the model is examined and it is noted that with a decrease in extra space the observable 3-D space entropy increase, thus accounting for the large value of entropy observable at present.