No, really, this is a fantastic question we should all ask more.

Because on the outside, in terms of space and the physical universe, it will undergo phase transitions, it will experience a long, slow cooling into rarified energy... but those terms "long" and "rarified" are just from our human reference frame. Roger Penrose's work demonstrated how even a vast, infinite expanding space with tiny particles zooming through it, from other reference frames behaves exactly like the big bang. IE: as the universe cools and expands, it's still infinitely dense and exploding outward from a different perspective of time and space. It's perpetual.

That's one thing. The other thing is this... time passing is meaningless if nobody is there to observe it. You will be dead for an infinite amount of time, you won't notice a moment of it. But every passing moment you're dead, the universe is rolling dice. It's always rolling dice.

Eventually, even if it takes so incredibly long that we don't have numbers to express it (we actually do) then something is bound to happen again. Eventually these "somethings" will be just right to create a kind of universe, complex information systems, and maybe even a consciousness that can experience it.

It sounds kind of fantastic and overly fanciful, but I am basing this on the evidence that it happened at least once before that we know of.

Try the Total Perspective Vortex.

I dunno, I feel like neither empty space nor vast aeons of darkness are particularly pulling their weight in terms of really doing existing with any real level of conviction. It's easy to be vast if you're doing fuck all with most of it.