The way I understand it, non-baryonic dark matter can be thought of as matter that interacts gravitationally but not electromagnetically with other matter. Is there a dual type of matter that interacts electromagnetically but not gravitationally? And if there is, or can be, such matter, can it exist at non- relativistic speeds? In other words, could you have stuff "massing" together through EM attraction but not subject to the gravitational force? Or is that such a basic violation of fundamental laws that it's excluded from consideration? Of course, maybe dark matter was considered as such before it was detected.