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I received the following question by email and thought others might also be interested in discussing it.
"It is widely acknowledged that the age of the universe is 13.5-14.0 billion years.
It is suspected that the boundary of the observable universe is further away, say 45 billion light years.
How can these two things co-exist in the domain of Big Bang and expansion? It seems that the boundary of the expansion has needed to move away at an average of around 3-3.5 times the speed of light for this to happen!"
Just after the end of the hypothesized inflation epoch, space itself was expanding so fast that two hypothetical light sources[1] at opposite ends of the present observable universe would have separated by an apparent 'speed' of larger than 1024c. Since they were not moving through space, there is no relativistic problem with that. This superluminal recession speed rapidly diminished as the inverse square law gravity retarded it.
The best models say those sources were only meters apart then, but today they are around 90 billion light years (ly) apart, 45 billion ly each way, with us in the center. It took the sources some 13.7 billion years to achieve that separation, for an average apparent recession speed (from us) of ~3.3c, as stated correctly in the question.
Now for a crucial bit of required insight: when the light that we today (hypothetically) observe from those sources were emitted,[2] they were only meters from our location (as stated above). However, due to the spatial expansion history, it took that light 13.7 billion years to cover the distance to us, moving precisely at c through local space.
For most of the 13.7 billion years, the photons were actually receding from us and it was only in the last 5 billion years or so that they actually made headway against the 'current' of expanding space. Remember that unlike a real current, expanding space 'flows' more rapidly the farther from us in any direction. Near us, there is no observable 'expansion current' today, but when the universe was young, even nearby 'currents' were strong.
I hope this answers the questions to some extent. Further questions are welcome and I will answer what I can, as long as we can stick to science and avoid philosophy.
-Jorrie
[1] There were no discreet light sources then, only super hot plasma everywhere and the tiny universe was not transparent to light. For ease of comprehension of the issue at hand, let's pretended that there were light sources and that the universe was transparent from the beginning.
[2] The farthest we can observe optically is the CMB, which is the first photons that could travel freely - when the 'fog' of the original plasma 'lifted'. This happened some 380 thousand years after the big bang.
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