it wouldn't take bardzo (wszechświat jest bardzo duży), I can't understand why.
Well, we usually accept "really" for "bardzo", so I guess it should be accepted the other way round. Added now.
I haven't tried entering it yet, but would "The Universe is truly big" be a possible translation?
I think that yes, although wouldn't it be a bit different in the shade of meaning? Like 'really big' is kinda like 'very big', but 'truly big' is like 'big indeed'?
They're more or less interchangeable, but truly/indeed could sound weird and off in some contexts.
I checked, it is accepted.
Could "Wszechświat to naprawdę duży" be correct, even if it seems somewhat casual?
No, that would be wrong. 'X to Y' only works with nouns on both sides.
Why is "Wszechświat naprawdę jest duży" wrong?
It means the same as "The Universe really is big" (as in "Woah, you're right, it really is big. I was wrong.").
Our sentence is almost the same as "The Universe is very big".
I feel that for "rzeczywiście" to be correct, it would need to be "really is big". "is really big" means basically the same as "is very big".
W rzeczywistości jest nieskończony.