See light that is red-shifting z > 5.4

[Ich]

Hmmm...

I really have problems understanding what they mean. The sentence

It relates the comoving distances for an expanding universe with the distances at a reference time arbitrarily taken to be the present.

$$l_p = l_t \; a(t)$$

where $\! l_t$ is the comoving distance at epoch $\! t$, $\! l_p$ is the distance at the present epoch $\! t_p$ and $\! a(t)$ is the scale factor.

could almost be correct if they chose nonstandard definitions.
If Lt is in fact a comoving distance taken at some reference time, then a(tp)*Lt is Lp, the distance now (tp).
However, they write a(t), which is wrong in this context. Further, you'd normally define Lp as the comoving distance, and relate it with the distance at a different time t -as you said.

I'll try to find a better wording for the article, or maybe you'd like to correct it?

 

[JesseM]

I'll try to find a better wording for the article, or maybe you'd like to correct it?

I had a go at correcting it, but feel free to modify further...

 

[Ich]

Better, but comoving distance is something different. The scale factor relates proper distance (Lp) with comoving distance (Lc): Lp= a*Lc.
Comoving distance is proper distance now.

 

[JesseM]

Better, but comoving distance is something different. The scale factor relates proper distance (Lp) with comoving distance (Lc): Lp= a*Lc.
Comoving distance is proper distance now.

Thanks, I edited it to distinguish between proper distance and comoving distance, and also edited the comoving distance article which discussed the proper distance but was missing that simple equation.

 

[JesseM]

Better, but comoving distance is something different. The scale factor relates proper distance (Lp) with comoving distance (Lc): Lp= a*Lc.
Comoving distance is proper distance now.

Hmm, but p. 263 of this book seems to say proper distance is something different from the scale factor times the comoving distance:

First it is important to remember that r in (10.23) is a comoving coordinate. If an observer here on Earth is at r=0 and a distant galaxy is at r=r_e, then the observer remains at r=0 and the distant galaxy remains at r=r_e. The term r is thus better thought of as a label than as a distance. The coordinate distance, d_C, is given by (10.20). If the light emitted by a galaxy with comoving radial coordinate r_e is observed by us at the present time t₀, then the present coordinate distance to the galaxy is given by

d_C(t₀) = R(t₀) r_e

where R(t₀) is the present value of the scale factor. The coordinate distance to the galaxy changes because R(t) changes, not because the galaxy has a large velocity through space away from us.

What is the actual distance to the galaxy? ... In the present context it is easiest to use the proper distance. To measure the proper distance to a galaxy, imagine that there is a chain of observers between us and the galaxy. Each observer measures the distance between himself and his immediate neighbor in the direction of the galaxy at the same cosmic time t. If we then add up all these small distance elements the result is the proper distance d_P to the galaxy at cosmic time t ... There are thus three expressions for the proper distance to an object, depending on the curvature of the universe:

d_P = R(t) sin^-1 r --- spherical
d_P = R(t) r --- flat
d_P = R(t) sinh^-1 r --- hyperbolic

Note that the proper distance is equal to the coordinate distance only in the case of a flat (i.e. k=0) space.

edit: On the other hand, p. 11-12 of this book distinguish between the "co-moving coordinate" r of a given galaxy and the function $$\chi(r)$$ which is multiplied by the scale factor to get the proper distance (defined at the top of p. 11 as the actual ruler distance), i.e. $$d_{proper}(r, t) = R(t) \chi(r)$$, with $$\chi(r)$$ working out to equal r when k=0 (flat universe), sin^-1(r) when k=1 (spherical) and sinh^-1(r) when k=-1 (hyperbolic). This mirrors the previous book but I am not sure whether r or $$\chi(r)$$ would normally be defined as the "comoving distance".

 

[Ich]

It depends on the coordinates you choose. What you have to do is to account for space curvature, where circumference/radius != pi. You may either scale the circumference or the radius in your coordinates, but you can't have both be "proper" coordinates if space is curved.
In http://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric#General_metric", you scale the radius, and that is what the book does. You have to unscale r to get proper radial distance, but you can use r*dphi directly to get tangential proper distance.
In Hyperspherical coordinates, you scale the circumference, and r measures proper radial distance.
I almost exclusively use hypersherical coordinates, so there's no ambiguity between r now and proper distance now.

 

[granpa]

So we can see light that is red-shifting z > 5.4 which means it would be moving faster than light speed away in relation to us. How can we see this? We couldn't see the object's light while the distance between us is increasing at more than light speed right? I realize the light we are seeing is billions of years old but having a z of more than 5.4 doesn't make sense to me. The only thing I can figure is that the space fabric itself is expanding while the light is traveling through it elongating the light more than when it started. Could anyone shed light on this. I feel really bad for making that pun.

cosmic microwave background is at z = 1100

 

[niceboar]

cosmic microwave background is at z = 1100

Yeah. But apparently light observed currently around 5.4 will reach us redshifted to infinity, so it won't. The cosmic radiation background would account for objects physically impossible to get light from anymore.

 

[mrspeedybob]

One simple way to understand why Hubble constant is decreasing: consider galaxy 1 Mpc away. It is receding from us at 71 km/s. Now, if value of Hubble constant remains the same, once it is 2 Mpc away it should be receding at 142 km/s, and so on. Our universe is accelerating in expansion, but not all that much.

Let me see if I understand this. 1Mpc away an object would be moving away at 71 km/s due to the expansion of space. 1 billion years from now a different object 1 Mpc away would be moving away at a lower rate, <71 km/s. Does this value ever go to 0 or <0?

 

[Calimero]

Let me see if I understand this. 1Mpc away an object would be moving away at 71 km/s due to the expansion of space. 1 billion years from now a different object 1 Mpc away would be moving away at a lower rate, <71 km/s. Does this value ever go to 0 or <0?

Yes, that is correct. In empty (or near-empty) universe it would approach 0 as $$t\rightarrow\infty$$. However in acclelerated expansion model, it should approach asymptotic value around 60.