The speed of gravity being limited to the speed of light is a prediction of Einstein's theory of general relativity. According to general relativity, gravity is not mediated by any particles in the way that forces like electromagnetism are mediated by photons. Instead, it is described as the curvature of spacetime caused by massive objects.
In general relativity, massive objects like stars and planets curve the fabric of spacetime around them, creating a gravitational field. Other objects moving through this curved spacetime are affected by this curvature, and their motion is influenced by the gravitational force.
The theory of general relativity predicts that changes in the curvature of spacetime propagate as gravitational waves. These gravitational waves are ripples in the fabric of spacetime itself and carry energy. Like any form of energy, they have a finite speed at which they can propagate, which is the speed of light in a vacuum.
The prediction of gravitational waves in general relativity was confirmed by the direct detection of gravitational waves in 2015, further supporting the idea that gravity propagates at the speed of light.
Therefore, while gravity is not transmitted through particles like photons, the bending and curvature of spacetime, which give rise to the gravitational force, propagate at the speed of light. This limitation is a fundamental consequence of the underlying geometry of spacetime in general relativity.