The Effect of Extra Dimension on Dark Matter

We investigate the thermal relic density of a cold dark matter in the brane world cosmology. Since the expansion law in a high energy regime is modified from the one in the standard cosmology, if the dark matter decouples in such a high energy regime its relic number density is affected by this modified expansion law. We derive analytic formulas for the number density of the dark matter. It is found that the resultant relic density is characterized by the ``transition temperature'' at which the modified expansion law in the brane world cosmology is connecting with the standard one, and can be considerably enhanced compared to that in the standard cosmology, if the transition temperature is low enough. The implication to the neutralino dark matter also is mentioned.