Hello: Aster's effects on goutweed is an interesting thought considering how invasive goutweed is. I haven’t been able to find any science based evidence discussing a non symbiotic relationship.

The following article pointed out goutweed is a perennial and propagates stoloniferous.

Aegopodium podagraria, (bishop’s weed, goutweed) perennial stoloniferous

https://www.extension.purdue.edu/extmedia/HO/HO-295-W.pdf

This is an excerpt from the article:

A stolon is a prostrate, horizontal stem that creeps along the ground and roots at the tip or the nodes. Each rooting site gives rise to a new plant. Plants that propagate by stolons make no effort to conceal their reproductive structures, yet they can be as expansive as plants with rhizomes. You can cut back stoloniferous plants as needed. They will generally dislodge from the soil surface more easily with a garden fork than their rhizomatous garden colleagues.

I’m not able to discover a reason why Asters may be preventing Goutweed from propagating, but I suspect the horizontal stem creeping along the ground may be prevented from penetrating the Aster perimeter.

It would be interesting to plant Asters where goutweed persists after best efforts to remove and observe the effects. I’m sorry I wasn’t able to find more information. If you are inclined to experiment, let us know how you make out.

Jeff - UVM Extension Master Gardener Helpline