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Motivated by the presence of numerous dark matter clumps in the Milky  Way's halo as expected from the cold dark matter cosmological model, weconduct numerical simulations to examine the heating of the disk. We constructan initial galaxy model in equilibrium, with a stable thin disk.  The disk interacts with dark matter clumps for about 5 Gyr. Three physicaleffects are examined : first the mass spectrum of the dark matter clumps,second the initial thickness of the galactic disk, and third the spatialdistribution of the clumps. We find that the massive end of the mass spectrumdetermines the amount of disk heating. Thicker disks suffer less heating. Thereis a certain thickness at which the heating owing to the interaction with theclumps becomes saturates. We also find that the heating produced by the modelwhich mimics the distribution found in  Standard CDM cosmology is significant and too high to explain theobservational constraints. On the other hand, our model that corresponds to theclump distribution in a $\Lambda$CDM cosmology produces no significant heating.This result suggests that the $\Lambda$CDM cosmology is preferable with respectto the Standard CDM cosmology in explaining the thickness of the Milky Way.Comment: 28 pages, 13 figures, submitted to Ap

Constraints of the Clumpiness of Dark Matter Halos through Heating of the Disk Galaxies