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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The answer to your question of why that didn’t fully explain gravity is because of space. An object has mass and therefore has gravity and then therefore pulls on other objects with mass so that they move towards each other.
The problem is that because space is _empty_ what does the actual pulling? You need something that acts like that rubber band or sheet the pulls the objects together. If you imagine two bowling balls on a trampoline what is the thing acting like the net?
We know that light moves like a wave (light particles spread out over space) but acts on matter at a single point (individual particles can only measured/captured at exactly one spot). We think gravity works the same way. It spreads out over all the space around the object with mass, but can only be felt by other discrete objects with mass/energy (light is also affected by gravity). We have taken measurements that show that gravity moves at the speed of light (thanks black holes!) so we can observe “ripples” in spacetime. Something must be communicating that gravity at the speed of light similar to photons and we call it, colloquially, “gravity waves”
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