That depends on what you mean by "know", I guess... According to the current best estimates of the cosmological parameters, yes, it is infinite. The basic theory could be wrong, of course, and outside the observable Universe the properties could be different.
That would have been the case if the universe was closed, i.e. if the matter density was above the critical density. However, the matter density is only about 20% of the critical, which means it's infinite. (The remaining 80% of the critical density seem to be the cosmological constant, which means the universe has flat geometry to within experimental error.)
