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Q:
According to Einstein's theory of relativity the slower objects move relative to other objects, the larger their relative mass. Would it be possible for some form of matter to be in the universe and not accelerated by gravity, therefore moving much slower than planets and stars, so in comparison this matter would seem to be more massive than if it was moving at the same speed as the other bodies? Then this matter could account for the extra "Dark matter" in the Universe.
A:
Any substance that is not accelerated by gravity is outside of Einstein's theory of general relativity. The dark matter has been detected by its gravitational effects, so we know that whatever it is, it is affected by gravity like every other object in the universe. We have a very nice explanation of the mystery of dark matter here:
http://chandra.harvard.edu/xray_astro/dark_matter.html
I think the special relativistic effect you are thinking of is actually the process of accelerating objects so that they are moving at speeds close to the speed of light, and as this happens they gain mass, or become heavier.
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