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It could be. But then again, if it is like this, it sure means the dark matter could not be described using the current physics.
Your idea is not that off, but it can't be glued with the rest of physics
I suspect that's a good definition of Dark Matter based on current understanding. Something that doesn't fit in the current laws.
That's what's so exciting, if we can find some way, any way, to interact with it other than gravity, we'll have something to base a new definition on, along with new laws of physics! ๐
Sadly as it only seems to interact via gravity, that might not happen and best we might get is a good mathematical model to describe it.
It's not that it doesn't fit. You can write whatever math you like.
But then you'll need to match it with observations. That's where the problem is. You can write a thousand of dozens theories that match the current observations, but they all will be wrong.
Here, for example, a pretty neat paper by an educated author that connects negative temperature with dark matter:
https://www.researchgate.net/publication/360324627_Dark_Energy_is_Dark_Matter_below_Absolute_Zero_in_Black_Holes .
What of it? It doesn't help humanity. Just another page in the almanac of what dark matter could potentially be