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Are you just wondering what 'pushing' means in this context? Or speculating about the existence of anti-gravity?
I'm pretty sure that this is just interpreting as region of low density as 'pushing' because it 'pulls less' than a region of average density would.
This is similar to how electron 'holes' in a metal's atomic lattice can be treated as positive particles.
It appears the article is showing an increase in speed from the low density region, a repulsion, as an addition to the attractors forces.
"that our galaxy is not only being pulled, but also pushed. In a new study in the forthcoming issue of Nature Astronomy, they describe a previously unknown, very large region in our extragalactic neighborhood. Largely devoid of galaxies, this void exerts a repelling force on our Local Group of galaxies.
“By 3-d mapping the flow of galaxies through space, we found that our Milky Way galaxy is speeding away from a large... (read more)