> It is a particular distributing of mass that solves the problem - typically, a highly specific distribution of mass
It's actually an extremely simple initial distribution of dark matter in the early universe. You can specify the entire distribution with one number: a spectral index. The thing is, we already know that the universe had that distribution of energy density anyways, because of the Cosmic Microwave Background.
If you take that very simple distribution and let the laws of physics run for 13 billion years, you get the required present-day distribution of dark matter. That distribution can be verified in several ways, including gravitational lensing, the rotation curves of galaxies, the motions of galaxies inside clusters, and the temperatures of hot gas inside galaxy clusters.
The fact that such a simple set of initial conditions can explain pretty much everything we can see on scales ranging from stars to the entire visible universe is why cold dark matter is overwhelmingly the favored paradigm.
It's actually an extremely simple initial distribution of dark matter in the early universe. You can specify the entire distribution with one number: a spectral index. The thing is, we already know that the universe had that distribution of energy density anyways, because of the Cosmic Microwave Background.
If you take that very simple distribution and let the laws of physics run for 13 billion years, you get the required present-day distribution of dark matter. That distribution can be verified in several ways, including gravitational lensing, the rotation curves of galaxies, the motions of galaxies inside clusters, and the temperatures of hot gas inside galaxy clusters.
The fact that such a simple set of initial conditions can explain pretty much everything we can see on scales ranging from stars to the entire visible universe is why cold dark matter is overwhelmingly the favored paradigm.