The statement that the speed of gravity is the same as the speed of light refers to the concept that gravitational waves, like electromagnetic waves (including light), propagate through space at the speed of light in a vacuum. This idea is consistent with Einstein's theory of general relativity.
Regarding the period of cosmic inflation in the early universe, it's important to note that the expansion of space during inflation is not subject to the same limitations as the motion of objects within space. During inflation, the fabric of spacetime itself expands at an extremely rapid rate, causing regions of the universe to move away from each other faster than the speed of light.
However, it's crucial to understand that this expansion of space is distinct from the motion of objects within space. The speed limit of light, known as "c," applies to the velocity of objects traveling through spacetime but not to the expansion of space itself. Inflation involves the expansion of space, rather than objects moving through space.
During inflation, various regions of the universe become separated by distances that grow faster than the speed of light, but this does not violate the principle that no information or objects can move through space faster than light. This is because the separation is due to the expansion of space itself.
After the inflationary epoch, the expansion of the universe slowed down, and objects within the universe, such as galaxies and other celestial bodies, are subject to the speed limit of light. Gravitational waves, as well as other forms of radiation and energy, propagate through this expanded space-time at the speed of light.
In summary, while inflation caused the universe to expand faster than the speed of light, this does not conflict with the idea that the speed of gravity and other forms of radiation is limited to the speed of light.