The farthest matter we will ever hear from

1. Feb 17, 2013

marcus

I guess most of us who frequent the cosmology forum are familiar with the idea that the farthest matter whose light we are now receiving (as the CMB) is around 45 or 46 Gly from here. Jorrie's calculator says 45.7.

That is the NOW distance, and it is used as a tag to identify all the matter in the model. Every bit of matter gets a permanent indelible "comoving distance" tag depending on how far away it is now (not how far it will be in future, or was at some time in past)

So we can ask questions in those terms. We can ask what is the distance NOW of the farthest matter that we will EVER get light from, assuming we stay around waiting forever.

The new version of the calculator tells you that, plus a lot of other things. It's something to get accustomed to using--you can learn quite a bit about standard model cosmology just playing around with it.
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo6.html

The rightmost column, the PARTICLE HORIZON, at each moment in time is the proper distance (the distance at that moment) of the farthest matter one could in principle be getting radiation of any kind from (e.g. gravitons as well as photons). The calculator says the particle horizon today (S=1) is 46.7 Gly. That's farther than the 45.7 Gly source distance of the CMB only because of opaqueness. The early universe was hot and dazzling so not transparent enough to let light more ancient than the CMB reach us. The particle horizon at any given moment is the true radius of the (theoretically) observable region, but we'd need better instruments to make it practical to see the extra depth.

The feature I want to emphasize in this thread is if you multiply the number in the leftmost column (the stretch factor S) by that in the rightmost (the particle horizon Dpar) you get the corresponding "comoving" or NOW distance.

So you can easily tell how far away NOW the most distant matter is, that we will ever hear from, or get any kind of signal from.

When you click on the calculator URL you get a table where the bottom row has S=.01 on the left and something like Dpar= 6230 Gly on the right. Just multiply the two and get 62.3 Gly---that's your answer.

The most distant matter that we will ever, in the whole history of the universe, get any kind of signal or radiation from, is NOW at a distance of 62.3 billion lightyears.

I checked that by adapting the table to approach S=.01 in small steps, say of size .01 or .02. Multiplying S by Dpar always gave essentially the same answer---around 62 Gly. The table had converged.

This is also what you see in the bottom band of Lineweaver's figure 1---link to which I keep handy in signature. You can see his particle horizon converge to around 62 Gly in comoving distance terms, as well.

Last edited: Feb 17, 2013
2. Feb 17, 2013

julcab12

Ah..., It's the 'NOW distance' all along. No wonder i'm getting the wrong idea (relief/sniff). Thanks Marcus!

3. Feb 17, 2013

Jorrie

Here is a much clearer graphic of the the bottom band of Lineweaver's figure 1 that Marcus referred to.

It is from the Tamara Davis 2003 doctoral thesis, page 8. I think she was the originator of the diagrams referred to. The figure also sports a very thorough caption, explaining all the diagrams.

For those not familiar with conformal time, it is a transformation that divides a proper time interval 'dt' by the the scale factor, i.e. $d\tau = dt/a$. The interesting thing about conformal time is that it makes the expanding spacetime appear 'flat' and it covers proper time from zero to infinity (because 'a' can go to infinity on the right-hand scale).

The three distance scales that Marcus referred to (CMB at 45.3 Gly, present particle horizon at 46.7 Gly and maximal particle horizon at 62.3 Gly) are all easy to spot on the diagram. Where the dotted gray line marked 1000 intersects the red light cone, move a little to the right (1100); there resides the CMB. The present particle horizon is where the red line reaches time zero. Beyond that we cannot presently observe anything by any means. The maximal particle horizon is where the yellow/gold area reaches time zero, beyond which nothing will ever be observable (unless there was something to be somehow observed before time zero. ;) There are probably 'things' in the gray zone, possibly extending to infinite distance, but we can never have any contact with them.

As time moves to the future, the light cone will shift upwards, but never quite reach the top, which is proper time infinity. Because of the 45 degree slopes, the diagram is actually cast in stone - all that would change if we should find that a need to revise our cosmological parameters, is the scale on the axes - that is unless we find that we have to also modify the LCDM model radically?

Attached Files:

• DavisConformaltimeDc.jpg
File size:
51.8 KB
Views:
140
4. Feb 17, 2013

Mordred

Nice paper definetely going to enjoy reading this. Good information on the calculator love the follow up explainations.