So we all heard about the twins paradox to explain einstein's time space relativity.
Wikipedia Quote :" In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly. "
So what if the universe has been travelling at varying speeds (increasing or descreasing), wouldn't this effect our measurements on age of the universe?
Answer
If the universe were non-homogenous, you'd have a point. But the key point of Robertson-Walker cosmology is that you fit the data very well by having a universe that is very nearly spatially homogenous. This means that, if each observer clicks of $T$ amount of time since the big bang, then they will all agree that there is no special point in the universe (like a center or an edge), and will all agree on the general geometry and shape of the whole universe.
Since you have this global time parameter, you don't get the effects you imply in your question. Everyone can agree on what $7 billion years after the big bang, at this point) means.
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