In article , David Staup
writes:

Is it possible that Dark Matter is repulsive to itself (by whatever
mechanism) while being attracted (by gravity) to normal matter?

Perhaps it is theoretically possible. For example, all DM particles
could be positively charged. (Of course, in this case, they would
interact electromagnetically and hence wouldn't be dark, but perhaps
there is some unknown repulsive force.)

It seems to me that that might explain inflation and the current
acceleration of expansion and a whole host of other observations.

No. The problem is that ORDINARY MATTER is observed in accelerated
expansion etc. If it were somehow being pushed apart by dark matter,
then this dark matter would have to couple rather strongly to ordinary
matter. However, this is not the case; the interaction cross section is
quite low, which is why there have been no (convincing) direct
detections yet.

It also wouldn't explain inflation in any real sense. Inflation has the
universe expand by several orders of magnitude in size. Any sort of
repulsive but otherwise normal matter would be thinned out too quickly
to have much of an effect.

In general, the idea doesn't solve anything: accelerated expansion
(whether now or during inflation) remains, but something unknown (dark
matter which is gravitationally attractive but self-repulsive) is
postulated for which there is otherwise no sort of evidence at all.

In general, there is too much emphasis on the "need for an explanation".
Not all of the universe is made of the same stuff we are. Big deal.
Isn't this what the basic expectation should be? Suppose it turned out
that most of the universe is made of the stuff we are (baryons); why
should this be? Wouldn't this be much more in need of an explanation?
As for accelerated expansion, the cosmological constant appears in the
equations of general relativity and has a value to be determined by
observation, just as the value of the gravitational constant is
determined by observation. (The fact that Einstein introduced the
cosmological constant for the wrong reason and later didn't like it is
historically interesting but not something the universe cares about.)
Note also that while GR can explain the equivalence of inertial mass and
passive gravitational mass, it can't explain the reason why an inertial
mass should have an active gravitational mass. It just does. Either
this demands an explanation as well (but hardly anyone seems to think
so), or one accepts the cosmological constant for what it is.