I have no introduction to the inflationary epoch. I know, however, that during this time space-time expanded with a speed faster than the speed of light. If gravitational waves are perturbations of spacetime how is it possible that their speed is limited by $c$ and at the same time there is no restriction, in terms of speed, on what spacetime itself is allowed to do?
Cosmology – Faster-than-Light Gravitational Waves and Expansion in Inflation
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Best Answer
This statement actually is the problem here. The expansion of the universe is not measured in units of speed, so it cannot really be compared to c in the first place. Saying that it is faster than the speed of light is “comparing apples and oranges”.
The expansion of the universe is currently about 70 (km/s)/Mpc. It was much larger in the inflationary epoch, but would still have the same units. So even then it does not make sense to compare the inflation rate to the speed of light. There is always a distance where the expansion between two points separated by that distance is less than c.
In contrast, the speed of a gravitational wave is an actual speed. Even on a local scale a gravitational wave travels at c. This is important because in GR only local speeds are physically meaningful. Speeds of things that are not colocated are not even well defined in a curved spacetime.
The speed of a gravitational wave is local, and therefore meaningful, and is c. The expansion of the universe is not a speed and cannot be converted into a local speed other than 0, so it is not meaningful and therefore cannot meaningfully be compared to c.