infinite. Scientists Haven't gone beyond what is limited for us. Just imagine, if our galaxy has us as life, and other planets, there must be billions of other galaxies and planets with their own kind of life. :)
The evidence we have, so far, teaches us all things have a beginning and end; that's what makes us ask the kind of questions you just ask. So scientifically speaking, space has to end somewhere and scientifically speaking, there must be something on the other side. No one knows what that is yet. So far this lines up perfectly with what the Bible teaches about the one true God. I believe God is at the end of our search for truth, but that's just me.