open closed flat confused about what universe counts

blumfeld0

hello. I know when omega is equal to, less than or greater than one our universe is either flat open or closed respectively.
omega is the ratio of the current observed density to critical denisty in the universe.
my question is that we can only see our part of the universe (that is 13 billion years old approximately) but the universe is actually much larger than that. we cant see it because light in that part hasnt reached us and some of it never will. there are particle and event horizons.
so when we calculate omega we are only looking at this part of the universe. but isnt the part greater than 13 billion years need to be taken into account to calculate observed omega. why is our part of the universe, up to our horizon, the important part to determine omegas value.
does this question make sense. i hope so
thank you

blumfeld

Jorrie

As you correctly stated, omega is a density ratio. If the universe at large is homogeneous and isotropic, then all we need to know is the density in one part and we know the density of the whole, is it not?

blumfeld0

yes you are right. thank you