The gravitational lensing evidence suggests massive and relatively dense accumulations of dark matter in space. However, dark matter collapsing to dense regions is unlikely due to energy conservation. Could there be a different explanation of how dark matter behaves? For example, is a matter - dark matter symmetry conceptually possible?
Consider the following scenario. For each type of a matter particle, there exists a corresponding dark matter particle. And also, for each type of a normal interaction, there exist a corresponding dark matter interaction. This way the dark matter behaves the same way as regular matter, perhaps with dark stars forming and emitting dark photons. However, the only interaction between matter and dark matter is gravitational through the curvature of common spacetime.
This way dark matter stars could co-exist with normal stars in the galaxy explaining the galaxy rotation. Also, some galaxies could be made predominantly of dark matter explaining the gravitational lensing.
Is there any reason why, for example, two diffeent electromagnetic interactions could not exist for two different types of matter without interacting with each other?