Testing Modified Dark Matter with galaxy clusters: Does dark matter know about the cosmological constant?

We discuss the possibility that the cold dark matter mass profiles contain information on the cosmological constant Lambda, and that such information constrains the nature of cold dark matter (CDM). We call this approach Modified Dark Matter (MDM). In particular, we examine the ability of MDM to explain the observed mass profiles of 13 galaxy clusters. Using general arguments from gravitational thermodynamics, we provide a theoretical justification for our MDM mass profile. In order to properly fit the shape of the mass profiles in galaxy clusters, we find it necessary to generalize the MDM mass profile from the one we used previously to fit galactic rotation curves. We successfully compare it to the NFW mass profiles both on cluster and galactic scales, though differences in form appear with the change in scales. Our results suggest that indeed the CDM mass profiles contain information about the cosmological constant in a nontrivial way.