In a recent podcast, the philosopher William Lane Craig said that while Special Relativity taught us to doubt whether any given clock is, or whether it could be, an absolute measure of time, General Relativity restored the possibility and perhaps evidence for a single "parameter": "Cosmic Time", which is the same for all frames-of-reference.
[...] what I point out in my published work is that when you turn to General Relativity then Absolute Time reemerges on a cosmic scale that was denied in Special Theory. So the Special Theory has been superseded by General Theory of Relativity. In General Relativity, there emerges a cosmic time, Kevin, that measures the duration of the universe from its inception. And this cosmic time is the same for every observer in the universe, regardless of his state of motion. It is not relative to reference frames or motion. It is frame independent (and in that sense absolute) and it measures the absolute duration of the universe.
Is this true? Have physicists found in General Relativity some evidence that there is in fact a single time parameter that both of the twins in the twins paradox, together with us and the most distant astronomical object, on our side and the distant side of the cosmological horizon... everything "knows" the true age of the Universe?