I understand that gravity is the curvature of space time. If that’s true, doesn’t it fully explain gravity? Why do we need gravity waves and/or gravitons?
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This is an answer to the second part of the question: why do we need gravitons?
We have two very good theories for describing how things work. For the very small, we have quantum mechanics, and the Standard Model of particle physics. This describes all the fundamental particles, how they interact, and what they can and can’t do. For very large things, we have general relativity, which describes the curvature of spacetime around massive objects. The problem is that these two models are incompatible. General relativity deals with exact positions and values, but quantum particles don’t have exact positions and values. According to quantum physics, every interaction is the result of a force-carrying particle, but quantum physics doesn’t describe a gravity-carrying particle. According to quantum physics, gravity shouldn’t exist. According to general relativity, gravity isn’t even a force.
So physicists made up a new particle, the graviton, to describe gravity. At first, it went pretty well. Then, it went less well. They discovered that for the graviton to exist, it needed to have properties never observed in an elementary particle before. We also can’t build a particle accelerator to detect a graviton, because gravity is such a weak force. If we built a particle detector the size of Jupiter and placed it next to a neutron star (the most dense non-black hole objects in the universe), we would expect to detect one graviton every ten years.
So physics is stuck. To understand how gravity is described by quantum physics, we need to measure the inside of a black hole. Which is impossible.
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