Brane world cosmological solution to the gravitino problem

We investigate the thermal production of gravitinos in the context of the brane world cosmology. Since the expansion law is modified from the one in the standard cosmology, the Boltzmann equation for the gravitino production is altered. We find that the late-time gravitino abundance is proportional to the "transition temperature", at which the modified expansion law in the brane world cosmology is connecting with the standard one, rather than the reheating temperature after inflation as in the standard cosmology. This means that, even though the reheating temperature is very high, we can avoid the overproduction of gravitinos by taking the transition temperature low enough. Therefore, the gravitino problem can be solved.