There is a very similar question to this one: Is dark matter really matter?. But the particular aspect I'm asking about seems not to be mentioned there. So, here we go:
Does dark matter have to exist as matter? Or, is it possible that space-time is just naturally not flat, but slightly crinkled? Obviously heavy objects can bend space-time, and if, as a layman, I understand it correctly, this is what we perceive as gravity. What now, if space-time is naturally not quite flat, and we perceive this non-flatness as dark matter?