But if the space-time manifold is expanding at faster than the speed of light, then we shouldn't be able to see the rest of the universe outside of our galactic cluster at all.
Because the photons emitted from those light sources would end up acting like photons trying to escape from a black hole. Wouldn't they?
That's why I'm confused.
These distant objects are either moving away from us at less than / equal to the speed of light, or more than the speed of light. If it's the former, then the light should have passed our location already. If it's the latter, the light should never reach us and the universe should be a sort of reverse event horizon surrounding us in every direction.
Light that is 13 billion odd years old must have been 13 billion light years away from us when it was emitted, if c is a constant. Right?
Only very widely separated points are beyond the observable horizon.
You'd think it's 13.7 billion light years to the horizon, but the space-time in between has expanded since the light was emitted, and the photons have lost energy as a result. In fact, depending on how you do the calculation, you can argue either that energy is lost or that it's been transformed.
At first glance, as the Universe is 13.7 billion years old, it seems natural to think that any object at a greater distance than 13.7 billion light-years will not be visible. However, as the Universe is expanding, photons in the cosmic microwave background (the first light emitted) have traveled approximately 45 billion light-years to get there: this makes the observable Universe about 90 billion light-years across.
This is the part I can't get my head around.
But the cosmic background radiation bit has also never made sense to me. If these microwaves date to the time of the Big Bang, then they all originated at a single point and all were emitted within the same narrow window of time. So how can it be "background" radiation? Shouldn't it be a thin hollow globe of radiation, like a glass Christmas ornament but made of microwaves, the size of the universe and expanding at the speed of light? And with nothing behind it, since the emissions of the Bang stopped at some point? Wouldn't you need a continuous radiator to have the radiation be distributed evenly as a "background"?
The microwaves (actually redshifted from much higher energy photons) date from the recombination time just after the end of the radiation era - about 300,00 years after the BB.
During the radiation era, the entire volume of the universe was dominated by radiation rather than by matter. So it was everywhere and not just a thin shell.