Let's consider a universe with constant expansion for simplicity's sake. In such a universe, the Hubble Parameter drops to half its value after double the time. If it happens to be 70 km/s/Mpc today, then it's the double, or 140 km/s/Mpc, when the universe was half its age 6.9 billion years ago, 280 km/s/Mpc 10.4 billion years ago and so on, you get the picture. Let's also assume that the "light" the observers see in this thought experiment is instant and any observers can somehow see everything as it is "now" no matter how far away it is.
We also know from Special Relativity that simultaneity is relative, it depends on the frame of reference of an observer. If the expansion of the universe only changes through time, but is constant throughout space, that's only true for a specific reference frame. An observer in that reference frame would see the Hubble Parameter in a specific region of space is always 70 km/s/Mpc now no matter how far away that region is, whether it's 1 billion light-years or 25 billion light-years.
However, for an observer moving at 0.5 c relative to that reference frame, his "now" is different when it comes to large distances. If you plot his motion on a Minkowski diagram, you'll find that his space axis, or "now line" is tilted 22.5 degrees relative to the stationary observer's space axis, in the direction he's moving in. This means, 25 billion light-years in front of him, his "now" is 12.5 billion years in the future relative to the "now" for the stationary observer's point of view of the same region. In a region of space 27.6 billion light-years in front of the moving observer, he would see the Hubble Parameter to be 35 km/s/Mpc, even if it's 70 where he is. Similarly, 13.8 billion light-years behind the observer, he'll see the Hubble Parameter is 140 km/s/Mpc. The moving observer will thus observe a younger universe behind him and an older one in front of him. This effect is only exaggerated the faster he travels. This effect exists in the real world, but what we see would be more complicated as light itself is not instant, unlike here.
This specific reference frame where the universe is the same age in every direction is apparently the reference frame of the Cosmic Microwave Background. Couldn't this reference frame be used as an "absolute" for asserting an universal time and an universal "now", which Special Relativity claims "doesn't exist"?
