Cosmology: Why do we think that the universe is expanding right now?

We think universe is continuously expanding because wherever we look, all the far-away galaxies show a red-shift, meaning that they are going away from us. But the light of those galaxies that we observe today is several billion years old since it took that look to reach us. Therefore, all we know is that those galaxies were moving away from us several billion years ago. So all we know is that the universe was expanding earlier.

Maybe it had stopped expanding at some point. Maybe the universe is contracting right now. We just don’t know yet!