Is the Higgs Boson Responsible for Gravity?

If the Higgs field was zero, would gravity be different at all? Or could the universe still make black holes and planets using gravity? It's an important thing to explore because a lot of people connect a concept of mass with gravity. But gravity is very deeply connected to energy and that includes mass. None of this would change the role of gravity at all. Gravity would still operate. It would still bend space. And you could still get black holes on all sorts of other stuff.