Where is the Cosmological Event Horizon in the LCDM model?

[marcus]

this is a case where it could be very helpful if someone (Pervect? Wallace? hellfire?) who has the numbers handy could tell us how far away the CEH is at present according to the usual LCDM model

I don't know the exact figure. I think it is somewhere around 16 Gly.

that is, slightly further out than the Hubble radius which is 13-14 Gly.

My feeling about dogma is that everybody gets to believe whatever they want about cosmology but that we should all UNDERSTAND the mainstream consensus model somewhat so we are all on the same page in discussions.

The mainstream LCDM may be just an effective model with parameters plugged into fit the data but it is impressively successful as such and if there is a more fundamental model lurking in deeper mathematical waters the LCDM will help guide us to it. Much respect for LCDM.

Well, one feature of LCDM is that it has a COSMOLOGICAL EVENT HORIZON somewhere out past the Hubble radius. A galaxy at Hubble radius (13-14 Gly) from us is receding at exactly c. But light from it can still reach us by a mechanism described in another YellowTriangle! thread. It can get here because H(t) is still decreasing slightly and will continue for a while more. H(t) decreasing means reciprocal--Hubble radius---increasing, so Hubble sphere can grow so as to reach out and take in light that is struggling to reach us but not making it, and then the light is home free.

but, according to LCDM, if a galaxy is significantly farther away than that, like say 16 Gly, then its light CAN NEVER REACH US IN ALL THE HISTORY OF THE UNIVERSE no matter how long we wait even until t = infty.

This is best communicated with a picture and Lineweaver 2004 paper has a picture. It is "Figure 1" in Lineweaver's "inflation and the CMB".

I will try to get a link to just that Figure 1 diagram, and also I'll paste in an exerpt from the article where he talks about it. The basic idea is pretty simple and easy to understand.

this is a basic feature of LCDM so my attitude is Nobody is forcing you to believe it. You can disbelieve that there is a CEH out there! You can believe any model you want with or without horizons. (In fact in the old CDM before 1998, there was no cosmological event horizon and all light that was aimed at us would eventually get here if you waited long enough! The coming of Lambda changed this.)

So nobody forces anybody to believe in a CEH but please let's all share some common familiarity with the main features of the consensus model.

I'd be glad if one or more experts would explain or discuss, and say actually how far away the CEH is.

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EDIT: The reason I said "The coming of Lambda changed this," in case anyone didnt notice, is that you only get a Cosmological Event Horizon if you have a POSITIVE LAMBDA, positive cosmological constant, or something equivalent that gives accelerating expansion.

The article by Lineweaver explains how the discovery of accel. expansion is what put the CEH into the picture.

Maybe I should have made this more explicit that it is thanks to the Lambda in LCDM. Or maybe that was obvious, I don't know.

Anyway the old CDM didnt have that feature.

 

[marcus]

Here's links
http://arxiv.org/abs/astro-ph/0305179
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/frames.html
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure1.jpg
This last link MIGHT give you a legible version of Figure 1 without having to get the whole article from Arxiv.
Here's an exerpt from the Lineweaver article that goes with the picture. There is a lot of extra stuff in this passage which helps establish context. I am not going to edit it out, just skim and get what you need. Or simply look at the picture:

==quote==
2.2 Inflationary Expansion: The Magic of a Shrinking Comoving Event Horizon
Inflation doesn’t make the observable universe big. The observable universe is as big as it is. What inflation does is make the region from which the Universe emerged, very small. How small? is unknown (hence the question mark in Fig. 2), but small enough to allow the points in opposite sides of the sky (A and B in Fig. 4) to be in causal contact. The exponential expansion of inflation produces an event horizon at a constant proper distance which is equivalent to a shrinking comoving horizon. A shrinking comoving horizon is the key to the inflationary solutions of the structure, horizon and flatness problems. So let’s look at these concepts carefully in Fig. 1. The new Λ-CDM cosmology has an event horizon and it is this cosmology that is plotted in Fig. 1 (the old standard CDM cosmology did not have an event horizon). To have an event horizon means that there will be events in the Universe that we will never be able to see no matter how long we wait. This is equivalent to the statement that the expansion of the Universe is so fast that it prevents some distant light rays, that are propagating toward us, from ever reaching us. In the top panel, one can see the rapid expansion of objects away from the central observer. As time goes by, Λ dominates and the event horizon approaches a constant physical distance from an observer. Galaxies do not remain at constant distances in an expanding universe. Therefore distant galaxies keep leaving the horizon, i.e., with time, they move upward and outward along the lines labeled with redshift ‘1’ or ‘3’ or ‘10’. As time passes, fewer and fewer objects are left within the event horizon. The ones that are left, started out very close to the central observer. Mathematically, the R(t) in the denominator of Eq. 8 increases so fast that the integral converges. As time goes by, the lower limit t of the integral gets bigger, making the integral converge on a smaller number – hence the comoving event horizon shrinks. The middle panel shows clearly that in the future, as Λ increasingly dominates the dynamics of the Universe, the comoving event horizon will shrink. This shrinkage is happening slowly now but during inflation it happened quickly. The shrinking comoving horizon in the middle panel of Fig. 1 is a slow and drawn out version of what happened during inflation – so we can use what is going on now to understand how inflation worked in the early universe. In the middle panel galaxies move on vertical lines upward, while the comoving event horizon shrinks. As time goes by we are able to see a smaller and smaller region of comoving space. Like using a zoom lens, or doing a PhD, we are able to see only a tiny patch of the Universe, but in amazing detail. Inflation gives us tunnel vision. The middle panel shows the narrowing of the tunnel. Galaxies move up vertically and like objects falling into black holes, from our point of view they are redshifted out of existence...
==endquote==
Here's more links. I'm finding it hard to get a link to a picture that is in large enough jpg format to be LEGIBLE.
The simplest is just to download the article from arxiv and print it out and turn to Figure 1. But I'm afraid many people will not have the time to do that so I want quick access to a clear picture of how the CEH fits in.
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver2.html

 

[MeJennifer]

Marcus, cosmological event horizons only exist in case of a positive cosmological constant.

 

[MonstersFromTheId]

MORE cool stuff to catch up on. Thanks Marcus.

 

[marcus]

MORE cool stuff to catch up on...

Monsters your interest is encouraging. I appreciate.
those videos I mentioned in the other thread are extremely technical but listening to some of the Ashtekar (and possibly some of Bojowald) could be helpful as giving a taste of current research and what goes on at workshops.

But the Lineweaver article linked-to in this thread is, I believe, quite a bit more accessible.

And especially, if you just have limited time, please have a look at this "Figure 1" link:
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure1.jpg

A picture can communicate ideas very fast.

Look at the top section (the figure is actually three diagrams plotting the same stuff with different time and distance scales) the top one uses the most natural intuitive scales.

Notice that the LIGHTCONE IS TEAR-DROP

it comes together at the bottom because the universe has expanded, so the far-reaching part of our lightcone goes back to when the universe was smallerscale. So the lightcone doesn't have the shape of a cone, it is shaped like a teardrop.

that is just one thing that one can get by looking at the top slice of Figure 1.

==================

another thing in the top slice, see the curve labeled "Hubble sphere"
that tracks what is also called the "Hubble radius" which is the distance away things are which are receding exactly at speed of light.
Out beyond that limit, stuff is receding faster than c.
Within that limit things recede slower than c.
(recession speed is a Gen Rel thing and not governed by Special Rel speedlimit)

notice how the Hubble radius (the curve labeled Hubble sphere) evolves
the fact that it has grown a lot in the past is why we are getting light emitted from things that were receding faster than c when they emitted the light.
It is tricky to see how that can happen, but the diagram can help.

Here's how to calculate the Hubble radius at any given moment (forgive me if you already did this, somebody might want to know)
like for example now at present time
the Hubble parameter is measured to be 71 km/second per Mpc
For every Mpc(megaparsec) distance you go out, the recession speed goes up by 71 km/s
So figure out how many Mpc you have to go out so that the recession speed is 300,000 km/s.
that must be 300,000/71 megaparsecs. That is the current Hubble radius

the Hubble parameter is very slowly decreasing and someday it will be only 70 km/s per Mpc
and then the Hubble radius will be bigger, it will be 300,000/70 megaparsecs.
and it will keep on increasing very slowly as it shows in the picture----Figure 1 shows the future too (as predicted by the usual LCDM model)

that Lineweaver picture is a big timesaver, you can learn a lot just by studying that one slice of it.