The Milnor-Wolf theorem states that any finitely generated solvable group has either polynomial or exponential growth. Is there an analogous result for locally compact compactly generated groups?

(or rather, for some smaller class of group? connected ones? connected Lie?)

Thanks!

The Milnor-Wolf theorem states that any finitely generated solvable group has either polynomial or exponential growth.

Is there an analogous result for locally compact compactly generated groups? (or rather, for some smaller class of group? connected ones? connected Lie?)