No, the universe is definitely finite, though the 'radius' of a 15 billion year old universe might be 40+ billion years thus the horizon is beyond our ever getting information from it. For all we know, the whole 'shebang' may be contracting at some where/when out beyond our information horizon, and in a few million or billion years, we'll be 'incorporated' in the 'renormalization' (collapse).
Make that diameter, not radius
Or everything will keep expanding until each tiniest particle is light-years from every other particle. And on and on expanding throughout eternity.