If dark matter winds up being roughly equally distributed in our solar system would this mean it has no net gravitational influence? Furthermore, do we expect dark matter to be less dense out in intergalactic space? Might this be because normal matter attracts it and gravitationally binds it?
Answer
Dark matter is pretty uniformly distributed on Solar System scales.
Yes, massive objects would attract it more. However, because it essentially does not interact with matter except through gravity, it will pass through stars and planets without stopping. Note that unless there is a collision to transfer energy, an unbound particle cannot become bound to a single mass, since it has too much energy. It will simply move on a hyperbolic trajectory, leaving the star/planet at the same speed it approached.
On the very largest scales (clusters of galaxies), dark matter and normal matter correlate positively.
Note that most of the gravitating mass in the universe is dark matter. If the Solar System had the same ratio of dark to normal matter as the universe at large, we would be dominated by it and there would be clear signs (e.g. the mass of the Earth would be nothing like the density of rock times its volume). Instead, we have a pretty typical dark matter density and an extremely high normal matter density (being on a planet close to a star is a very rare find if you randomly picked points in the universe).
See also this answer for further discussion and references.
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