Why can’t we observe all regions of the universe?

[Astro Santi]

Homework Statement

I am trying to understand the concept of the observable universe and why there are regions whose light has not yet reached us, despite the universe having a finite age (~13.8 billion years).

Relevant Equations

Hubble’s law:

v = H₀d

My understanding is that light from distant regions has been traveling toward us since the early universe. Therefore, if the expansion rate of the universe were always less than the speed of light, I would expect that we should eventually receive light from all regions.


However, I have read that some regions are receding from us faster than the speed of light due to the expansion of space itself, and that this prevents their light from ever reaching us.


I find this confusing because it seems to contradict the idea that nothing can move faster than light.

So my question is:
How does cosmic expansion allow regions of space to become permanently unobservable, and how is this consistent with the relativistic limit on the speed of light?

 

[Ibix]

The rule that "nothing can travel faster than light" is a local rule. Nothing will ever overtake a pulse of light, that is true. But answering the question "how fast is that thing over there going relative to me" (i.e., measuring the speed of something not local to you) turns out to be a messy and complicated topic in curved spacetime, and the answer can be greater than the speed of light. So yes, the distance to distant galaxies is increasing faster than the speed of light (because that isn't a speed in the relevant sense). But light will always win a race over any distance in the universe.

I'd recommend Davis and Lineweaver's paper on common misconceptions about the expanding universe. Figure 1 lays out what's going on here, and section 3.1 talks about "faster than light expansion".

 

[A.T.]

I find this confusing because it seems to contradict the idea that nothing can move faster than light.

There is a difference between moving through space (which is limited by c) and expanding space (which can increase the distance between two distant objects faster than c).