wolram said:
Where is the boundary that light will never reach us, ...?
Wooly the others (Mfb, Mordy et al) already answered, but I like your question a lot and Mordy just posted a useful table based on latest data from the ESA (euro. space. agency) Planck mission so it's hard to resist talking more about this!
There are two questions:
A. where is the matter whose light will never reach us?
B. where is the matter whose light emitted today will never reach us?
Answers:
A. The matter whose light (even light it emitted long ago near start of expansion that has already been traveling 13.7 billion years towards us!) will never reach us is now at or beyond distance 63 billion LY. The cutoff is 63 Gly. Light that set out in our direction long ago from matter that is now less than 63 Gly will eventually get here.
That is also the matter that light from OUR stuff, emitted long ago near start of expansion, will eventually reach. It works both ways. You get that number from Mordy's table by going to the a=100 row (bottom row) and looking at "particle horizon, D
par" which is 6259 Gly and dividing by a=100.
6259 Gly what the distance to that matter will be when light from our stuff eventually gets there, and it is 100 times what the distance to that matter is now. So divide by 100 to get the distance of that matter now, something around 63 Gly.
B. The matter whose light (emitted TODAY) will never reach us is now at or beyond distance 16.47 Gly. You get that number from Mordy's table by going to the a=1 row (the present day row) and looking at "event horizon D
hor" which you see is 16.47 Gly. Let's call that 16.5 billion ly, not to be overly precise.
If TODAY a galaxy which is 16.5 Gly from us has a supernova explosion we will never see it.
But a galaxy closer than that cutoff can have an explosion today or send us a message today and we WILL eventually see it. Again, it works both ways. Closer than 16.5 are where the people are to whom we could today send a message and it would eventually get there. The people beyond 16.5 are folks we could not reach with a flash of light signal that we send off today. That's called the cosmic event horizon.
The cosmic "event horizon" is NOT THE SAME as the "Hubble radius" denoted R in the table. The current size of the Hubble radius, if you look on the a=1 row, you see is 14.4 Gly. That is the distance of light which is trying to get to us but not making any progress because it is traveling thru space which is receding at exactly c. And light that is now safely WITHIN 14.4 is making progress towards us.
You can see from Mordy's table that the Hubble radius increases over time. You can also see that from the curves plotted in Jorrie's post which I just saw.
Light which is today at Hubble radius 14.4 will EVENTUALLY make it because even though it is making no headway now the size of the Hubble radius will eventually grow to take it in, and then it will be within Hub radius and begin to close in on us. A lot of people are puzzled by this. How can light which is currently in space receding at speed c and making no progress eventually get here? You mean to say that the Hubble radius is not an horizon?
This confusion of people is very natural and something we just have to live with.
Like I said the REAL event horizon distance (as of today) is not the Hub radius of 14.4 but the one the table shows as 16.47. A photon that is today just barely within that distance, and aimed at us, will indeed be slowly losing ground and getting swept slowly back, but way in the future it will have been swept back only as far as 17.3 and just as it is almost lost ("falling over the cliff" so to speak) the Hubble radius, which has been increasing faster than the distance to the photon, will also extend out to 17.3 and take it in! Saved at that last moment! On the very brink of despair! So the REAL horizon, as of today, is 16.47
Mordred said:
The link above is an older version of Jorrie's calculator the latest version is at although the latest link is included in that thread it would take a bit to find it. here is the latest version below
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
I simply selected the columns I wanted, used the text script small the value you want is at S=1.000 D
hor you can see later on that the maximum distance we will ever receive light will be in the future when D
hor equals 17.3 Gly proper distance
{\small\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}} {\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly) \\ \hline 0.001&1090.000&0.0004&0.0006&45.332&0.042&0.057&0.001\\ \hline 0.003&339.773&0.0025&0.0040&44.184&0.130&0.179&0.006\\ \hline 0.009&105.913&0.0153&0.0235&42.012&0.397&0.552&0.040\\ \hline 0.030&33.015&0.0902&0.1363&38.052&1.153&1.652&0.249\\ \hline 0.097&10.291&0.5223&0.7851&30.918&3.004&4.606&1.491\\ \hline 0.312&3.208&2.9777&4.3736&18.248&5.688&10.827&8.733\\ \hline 1.000&1.000&13.7872&14.3999&0.000&0.000&16.472&46.279\\ \hline 3.208&0.312&32.8849&17.1849&11.118&35.666&17.225&184.083\\ \hline 7.580&0.132&47.7251&17.2911&14.219&107.786&17.291&458.476\\ \hline 17.911&0.056&62.5981&17.2993&15.536&278.256&17.299&1106.893\\ \hline 42.321&0.024&77.4737&17.2998&16.093&681.061&17.300&2639.026\\ \hline 100.000&0.010&92.3494&17.2999&16.328&1632.838&17.300&6259.262\\ \hline \end{array}}
