# Cosmic Horizon and Surface of Last Scattering Question

1. May 16, 2013

### Salamon

I have been watching Susskind's lectures on Cosmology which are great. There is something that I can't wrap my head around.

I know that if we look far away enough into the past (about 100,000 years after the big bang I think he said) , the radiation that is being emitted comes from plasma and as a result blocks any light from getting to us from beyond. This is what I understand to be the surface of last scattering.

I also get that the Hubble law states that v = Hd and as the Hubble constant approaches a constant value, there exists a cosmic horizon defined by d =c/H such that any object that passes this distance will not be observable since it would have to send a message at faster than the speed of light in order for us to observe it.

I think Susskind said that the surface of last scattering would always be within our cosmic horizon. How can this be if the cosmic horizon remains fixed?
If the deonized gas which makes up the surface of last scattering is moving away from us at a faster and faster rate, won't it eventually move beyond the cosmic horizon?

Where am I messing up? What I am visualizing wrong?

Thanks.

2. May 16, 2013

### Bandersnatch

Just one thing: the gas was everywhere when it stopped being opaque to radiation.

It's not an object that recedes from us while continuously emitting radiation. The radiation was emitted once, from every point in space. That ensures there is always some radiation passing the cosmic horizon, even as it gets more and more stretched by the expansion.

(and I think it was ~380 000 years, not 100 000, iirc)

3. May 16, 2013

### Salamon

Thank you. You helped clear things up for me a lot.

4. May 16, 2013

### Chronos

The CMB will be visible to us until it redshifts beyond detectability [which will not happen for a very long time]. There is, however, a boundary beyond which any light emitted at our present time will never reach us. It is called the cosmic event horizon. The size of this horizon is dependent on the dark energy density [w], currently believed to be w = -1. At this value the horizon will maintain a constant size of about 16 billion light years, meaning that light currently being emitted by any object with a redshift greater than about 1.7 will never reach us.

5. May 16, 2013

### marcus

There are two horizons cosmologists often mention the cosmic event horizon which is about light emitted TODAY and the particle horizon which is the size of the currently observable portion of the universe---the farthest matter which we could in principle be getting radiation from.

The surface of last scattering is now, and will always be, within the particle horizon.
But it is now, and will always be, way beyond the cosmic event horizon (CEH).

In this table, the CEH is called Dhor and the particle horizon is called Dpar
This table runs from a time in the past when distances were 1/10 present size, out to a time in the future when distances will be 10-fold present size.$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.100&10.000&0.5454&0.8196&30.684&3.068&4.717&1.558&2.13&3.74\\ \hline 0.126&7.943&0.7707&1.1568&28.684&3.611&5.687&2.213&1.99&3.12\\ \hline 0.158&6.310&1.0886&1.6308&26.444&4.191&6.804&3.141&1.84&2.57\\ \hline 0.200&5.012&1.5362&2.2939&23.938&4.776&8.066&4.455&1.66&2.08\\ \hline 0.251&3.981&2.1646&3.2127&21.143&5.311&9.452&6.310&1.47&1.65\\ \hline 0.316&3.162&3.0412&4.4626&18.045&5.706&10.920&8.924&1.25&1.28\\ \hline 0.398&2.512&4.2500&6.1052&14.651&5.833&12.396&12.585&1.02&0.96\\ \hline 0.501&1.995&5.8828&8.1349&11.008&5.517&13.780&17.670&0.76&0.68\\ \hline 0.631&1.585&8.0151&10.4035&7.226&4.559&14.962&24.632&0.50&0.44\\ \hline 0.794&1.259&10.6685&12.6018&3.483&2.767&15.863&33.982&0.24&0.22\\ \hline 1.000&1.000&13.7872&14.3999&0.000&0.000&16.472&46.279&0.00&0.00\\ \hline 1.259&0.794&17.2572&15.6486&3.109&3.914&16.842&62.157&0.22&0.25\\ \hline 1.585&0.631&20.9561&16.4103&5.731&9.083&17.047&82.407&0.40&0.55\\ \hline 1.995&0.501&24.7888&16.8364&7.890&15.743&17.153&108.052&0.55&0.94\\ \hline 2.512&0.398&28.6942&17.0630&9.638&24.210&17.204&140.420&0.67&1.42\\ \hline 3.162&0.316&32.6380&17.1800&11.040&34.912&17.224&181.213&0.77&2.03\\ \hline 3.981&0.251&36.6015&17.2395&12.160&48.409&17.240&232.590&0.84&2.81\\ \hline 5.012&0.200&40.5748&17.2696&13.051&65.411&17.270&297.281&0.91&3.79\\ \hline 6.310&0.158&44.5532&17.2847&13.760&86.821&17.285&378.728&0.96&5.02\\ \hline 7.943&0.126&48.5341&17.2923&14.324&113.777&17.292&481.267&0.99&6.58\\ \hline 10.000&0.100&52.5163&17.2961&14.772&147.715&17.296&610.357&1.03&8.54\\ \hline \end{array}}$$

The online version of the the table is interactive and self-explanatory. Go here:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
and hover the cursor over the blue dot next to various quantities, to get an explanation.

You can see that the CEH is now 16.47 billion LY, and it is increasing slowly towards a limit of 17.3 billion LY. Today, if the distance to a galaxy is less than 16.47 Gly then we could fire off a message to them which would eventually reach them. But a farther galaxy not.

The surface of last scattering, the matter that emitted the ancent CMB light we are currently getting, is now at a distance of some 45 or 46 billion LY. The theoretical limit, the distance we could in principle be getting light from is just slightly farther, still around 46. You can see that in the table, in the middle row labeled a=1 (the present). Dpar=46.279 Gly.

The present-day distance of the absolute farthest matter we will EVER get light from is between 62 and 63 Gly (as of TODAY). You can kind of see that from the table if you look at the bottom row.
In that day far in future (when distances are 10-fold today's) the Particle horizon of future Earthlings, roughly the same as the surface of last scattering as seen by them, will then be 610 Gly. But today the same matter is 61 Gly from us (and of course the light they will receive is already on its way here.) You can see the ratio Dpar/a converging to around 62 or 63---that is the distance now of the farthest matter which they, in that future time, could be getting light from. It is the ultimate limit of the observable portion of the universe.

I suggest you try out the online table calculator and learn to interpret some of the columns. There is a lot you can learn from it and it will supplement any good cosmology lectures you might watch.

Last edited: May 17, 2013