Yet negative pressure could drive expansion, and at the very least is postulated by Guth to have driven inflation. If the universal vacuum energy 'hung up' at a false ( higher than ) zero level just after the big bang, it would have experienced violent inflation while it slowly fell to the actual zero point vacuum energy. If it never actually reached the zero point, but just drastically slowed down its descent ( much lower slope ), then it could still be driving expansion at a much reduced rate, ie. accounts for the cosmological constant.
But I guess that unless we can get a handle on a realistic value for the vacuum energy, all this is just speculation,