Gooday John,
Welcome to Ice in Space, hope you visit us more often, lot of friendly and intelligent people here, who are very helpful.
As for your question, I am definitely no expert on this subject but I believe the current theory/hypothesis is this thing called Dark Energy that is driving the Universe expansion. As for it filling in an empty void, I don't think that's correct, the empty space itself is expanding (at the speed of light) and dragging the physical stuff along with it.
To wet your appetite here is a link from our ABC that can make your brain hurt. But use google to hone in what else you need to know.
http://www.abc.net.au/news/2016-01-2...iverse/6994612
Cheers
Bill