What is on the outside of our universe?
As of now, there is no preferred center for our expanding universe. What is expanding is space and not the matter. So, in my opinion, the definition of outside of our universe is not yet definitive..
There is no absolute frame of reference to fix any direction. The definition of a direction is local and not for the expanding universe.
There is no preferred center about which our universe is expanding evenly like
'Rate of change of volume of a sphere is the surface area'.
I had generalized this for higher dimensional hyper sphere, long long ago. In view of all these being inapplicable for expansion of our universe, any definition of 'outside' of our universe' is not definitive.
Up on having a consensus definition of 'outside of our universe',. the discussion on what is outside could be taken up.