Is the speed of expansion of the universe faster than light?

[JDoolin]

The quantity [physical distance/time] is increasing for the light ray.

[Physical distance= a[t]*comoving distance[comoving distance=coordinate distance between labels that do not change with time]]

Is it increasing in the diagram? If I understood the idea correctly, we have:

$$c^2 d\tau^2 = c^2 dt^2 - a(t)^2 dx^2$$

which simplifies to:

$$c^2 = \frac{a^2 dx^2}{dt^2} \overset ? = constant$$

which would be the speed of light (squared) when using the physical distance.

But the speed of light (squared) in the comoving distance would be

$$\frac{dx^2}{dt^2} = \frac{c^2}{a(t)^2}$$

which would be slowing down as a(t) increases.

(Edit: Now that I look at the diagram again, it does appear that the physical distance speed of light is increasing, i.e. $c^2 = \frac{a^2 dx^2}{dt^2} \neq constant$. Is that a particular feature of the Lambda-CDM model, or is it just a badly drawn speed-of-light line?)

 

[bcrowell]

The mentors have discussed this thread and decided that it is time to close it. Please note that we have a FAQ entry on this topic: https://www.physicsforums.com/showthread.php?t=508610