Is there any difference between the following sentences?
We do not know what dark matter is at the moment.
We do not know what dark matter is for the moment.
I cannot see any diffetence. Is there any?
There is a difference.
At the moment is used to mean at present, at this time, at this second. So if someone asked whether you wanted to go for a walk you might well reply:
Not at the moment, thank you.
However, you might well be in the mood for a walk later.
For the moment is an expression that means for now. It is often used in situations when someone is busy with a task that is uncompleted, as in:
The flower arrangement is not perfect but it will do for the moment.
I have not quite finished tidying the room but it looks okay for the moment.
The are not exactly friendly but they are getting along for the moment.
Depending on the context, the implication is that the task is not quite finished or that things may well change in future.
Both can mean the same thing, but there is a slightly different connotation.
For the moment can imply, but does not have to imply, that there's a likelihood that it'll change. We do not know what dark matter is, for the moment would imply a but we will, someday sort of thought.
At the moment or at this moment tends to be more explicitly about exactly that moment. We do not know what dark matter is at this moment would be a better answer to the question what is dark matter? without thought about whether we'll figure it out down the road.
In the end, though, both can be used interchangeably. The very small difference is, well... very small.