Planck's summer: particle size matters!

second post in the “Planck’s summer”-series by Youness: Let us assume that dark matter is made of approximately collisionless particles evolving under the laws of gravity (just one type, for simplicity). Is there a minimum mass \(m_\text{min}\) these particles need to have in order to fit observational constraints? Conversely, is there an upper limit \(m_\text{max}\)?