Position of Earth in the Universe

[Chronos]

Consider, as well, that as space stretches [expansion] so do the light waves traversing it [redshift]. All objects presently observable will always be observable, albeit, as ST noted, they may eventually become redshifted beyond detectability.

 

[oldman]

I'll assume that by "constant rate", you mean that the Hubble Constant is constant. Again, your statement is incorrect if your "Horizon" is meant to refer to the edge of the observable universe. The event horizon never provides this boundary. The lack of a particle horizon would mean that someone in this universe could, in theory, observe any part of the universe if there were no physical screen (like the surface of last scattering).

I stand corrected. In the toy model I was describing the integral defining the event horizon radius diverges logarithmically with time, so there is no event horizon. One just has to wait an extra-long time to see everything.

There is one relevant complication -- inflation. Whenever we talk about the particle horizon in cosmology, we're usually only integrating back to the beginning of inflation, not to t=0. We have virtually no information about the universe prior to inflation, so our "true" particle horizon, inflation included, could even be infinite. However, the universe expands many times over during inflation (order 100 e-folds), so any information about the universe prior is redshifted or diluted into unobservability.

But, during inflation, the integral converges because of exponential expansion, and there is an event horizon. Here the anaysis I gave in post #12 is, I hope, correct, and the horizon problem is solved by an interaction between horizons, as I described.

The surface of last scattering could also be called a complication, because it effectively screens us from observing anything prior to z=1100, but that assumes we're observing with light. Using neutrinos, we could go as far back as z~10⁹. These limits are also easily incorporated into the calculation by just changing the lower limit of the integral.

I agree.

 

[SpaceTiger]

I stand corrected. In the toy model I was describing the integral defining the event horizon radius diverges logarithmically with time, so there is no event horizon. One just has to wait an extra-long time to see everything.

The behavior of the universe under a constant Hubble constant is the same as that under inflation, so there is an event horizon. What I think we disagree on is the definition of the event horizon. It doesn't describe how much of the universe we can see now, it describes how much of the universe that will eventually be able to see us (as we are now).

 

[oldman]

The behavior of the universe under a constant Hubble constant is the same as that under inflation, so there is an event horizon. What I think we disagree on is the definition of the event horizon. It doesn't describe how much of the universe we can see now, it describes how much of the universe that will eventually be able to see us (as we are now).

We can't disagee about the definition of event horizon; I must accept the way it is defined in cosmology.

 

[marcus]

We can't disagee about the definition of event horizon; I must accept the way it is defined in cosmology.

how, in your experience, is the "cosmological event horizon" defined by cosmologists?

In my experience they do not equate "cosmological horizon" with "Hubble sphere". Probably also in your experience reading mainstream cosmology works.

More notably, the cosmological horizon is also AFAIK NOT EQUATED with the particle horizon!

I am trying to recall the exact figures from a standard pedagogical work like Lineweaver "Inflation and the CMB". Roughly, IIRC, in terms of the Hubble-Law distance-----the distance of objects at this present moment which one plugs into the Hubble Law to get the present recession speed--- one has something like:

hubble radius = approx 14 billion LY
particle radius (edge of currently observable) = 47 billion LY
distance to cosmological event horizon = 62 billion LY

when I get a moment I will find the Lineweaver paper and check. Meanwhile maybe SpaceT or others will correct any error.

http://arxiv.org/astro-ph/0305179

Yes, these are Lineweaver's figures, see Figure 4 on page 13, and also this on page 14:

"... the full size of a causally connected patch, although bigger than the observable universe, will never be known unless it happens to be between 47 Glyr (our current particle horizon) and 62 Glyr (the comoving size of our particle horizon at the end of time). ..."

The cosmological event horizon is the estimated distance to the furthest galaxy which will ultimately be visible if one is prepared to wait out to "year infinity". You can see in Figure 4 that it is labeled "event horizon". I think this is for brevity---the full name is "cosmological event horizon" but one sometimes sees it called event horizon or cosmological horizon, for short.

In any case it is NOT equal to the present edge of the observable universe.

The estimates based on the consensus Lambda CDM model with usual values of parameters.

I hope this post is superfluous and that you and SpaceT already understand and agree on what you mean by "cosmological event horizon". I would agree that it is a good idea to accept prevailing definitions of terminology used by working cosmologists (or, in cases when this is not consistent, to define oneself the terms one uses.)

 

[Garth]

The Particle horizon is our limit of observation now.
We cannot see beyond it today.

The Event horizon is our limit of observation for all time in the future.
We will never be able to see beyond it - no matter how long we wait.

Garth

 

[SpaceTiger]

hubble radius = approx 14 billion LY
particle radius (edge of currently observable) = 47 billion LY
distance to cosmological event horizon = 62 billion LY

The first two are right, but I disagree with the last one. I think that's the size of the particle horizon at t=infinity. The current event horizon in \Lambda CDM is approximately the same size as the Hubble radius (see Figure 1 of the Lineweaver paper you cited and note the line marked, "Now").

The cosmological event horizon is the estimated distance to the furthest galaxy which will ultimately be visible if one is prepared to wait out to "year infinity".

This description (and Garth's) make it sound like the particle horizon for an observer at t=infinity. The event horizon is a time-dependent quantity (in fact, it shrinks with time in \Lambda CDM), so there must be something more to consider.

Let's step back a bit and try to get a cleaner conceptual picture. Since many of the readers might be unfamiliar with comoving coordinates, I'll return to the balloon analogy. Imagine we're on the surface of an expanding balloon and stuck to that balloon are a bunch of pennies, which will represent galaxies. We're living on one of those pennies and want to ask the question, how many other pennies can we see? Since it will take time for light to travel to us from these pennies, the answer will depend on when we're looking. This is the idea behind the particle horizon.

We can ask another question, however. Suppose our penny changes, perhaps Abe Lincoln grows an afro, how many other pennies will be able to see this event at some time in the future? Or, equivalently, if another penny gets an Abe-afro, how close do we need to be to see it? The answer to either of these questions will be the event horizon (or a quantity simply related to it). Like the particle horizon, the event horizon is time-dependent, but it depends on the time of the event rather than the time of the observation.

The current event horizon tells us about what current cosmic events we will be able to see in the future. It tells us nothing about what we can presently see.

 

[marcus]

I understand what you mean.
An event is going to happen right NOW at this moment. If it is too far away, then no matter how long we wait we will never see it (because of how the LambdaCDM model expands)

So the question is, how far away could the event be and we still eventually see it happen, assuming we can wait indefinitely.

I think that is what you say is meant by the event horizon, and it looks like in the Lineweaver article, figures 1 or 4, that it is only slightly more than 14 billion LY.

only slightly more than the Hubble radius.
================

in the past I had the idea that the event horizon was, as Garth seems to be saying, the present distance of the farthest stuff whose light will ever reach us------including light already emitted and already on its way towards us.

this one can read off the figure 4 and being about 62 billion LY.

**The cosmological event horizon is the estimated distance to the furthest galaxy which will ultimately be visible if one is prepared to wait out to "year infinity".**

This description (and Garth's) make it sound like the particle horizon for an observer at t=infinity. The event horizon is a time-dependent quantity (in fact, it shrinks with time in ), so there must be something more to consider.

what you say here is right:
"This description (and Garth's) make it sound like the particle horizon for an observer at t=infinity."

that is exactly what I thought event horizon meant. I've now checked several sources and conclude that your definition is the one generally used. Goes back to a 1977 article by Gibbons and Hawking (at least, maybe further)

So 62 billion LY is the current max distance of matter that we can eventually get light from and thus learn something about. there is no snappy conceptual name for this 62 billion LY distance that I know of.

But the "event horizon" is approximately 15 billion LY (give or take some) and it is the current max distance of matter which, if it did something TODAY, we could eventually learn of the occurrence of that something.

 

[Chronos]

I'm easily confused. The surface of last scattering is a logical barrier to any future observations IMO [i.e., we already see all of the observable universe that will ever be possible to observe] I don't see that ever going away. I allow, however, that a neutrino telescope could peer beyond that barrier.

 

[marcus]

I'm easily confused. The surface of last scattering is a logical barrier to any future observations IMO [i.e., we already see all of the observable universe that will ever be possible to observe] I don't see that ever going away...

Consider that this could be a mistake Chronos, because
the surface of last scattering is moving back away from us with lightning rapidity

as it moves away, we have inside this sphere of last scattering always
more and more of the universe, for us to observe and learn about, more and more galaxies, more and more regions of galaxy formation,

this statement is not true:
" [i.e., we already see all of the... universe that will ever be possible to observe] "

So far what I am saying makes no reference to neutrinos. I am talking about light.

 

[oldman]

how, in your experience, is the "cosmological event horizon" defined by cosmologists?... I would agree that it is a good idea to accept prevailing definitions of terminology used by working cosmologists (or, in cases when this is not consistent, to define oneself the terms one uses.)

This post of yours has greatly clarified the horizon situation for me, Marcus. The Lineweaver article, which I have downloaded but not yet finished, is especially helpful. I was gratified to find that he makes the point that:

"A shrinking co-moving horizon is the key to the inflationary solutions of the structure, horizon and flatness problems".

This is just the point I had figured out and made in my post #12. I also now understand from your, Space Tiger and Garth's posts why cosmologists place emphasis on the particle horizon rather than on the event horizon -- which is after all a far-future pie-in-the-sky affair (except in inflation).

But I do still have trouble with the effect of horizons on phase changes. When inflation stops, it is proposed that the false vacuum is transformed into the true vacuum. This is a very sudden change of phase. How does the message "change phase now" spread through the large inflated universe, and is its spread not confined by an horizon, like any other message conveyed at c?

 

[hellfire]

The number 62 Gly is the size of the particle horizon in the standard model of cosmology at t \rightarrow \infty measured in comoving coordinates. However, this particle horizon always grows in proper coordinates, Dp = a(t) Dc. A particle horizon remaining at constant comoving distance from us means that no new objects can enter it, regardless from the fact that it always grows in proper coordinates, because in an homogeneous and isotropic expanding universe objects are always at constant comoving distances from us (peculiar speeds can be neglected).

 

[Jorrie]

Cosmological event horizon

Good stuff... maybe one of you knowledgeable guys want to update Wikipedia's definition of the cosmological event horizon:

The event horizon is defined as the largest comoving distance from which light can ever reach the observer — at any time in the future.

Its under http://en.wikipedia.org/wiki/Particle_horizon

 

[marcus]

Good stuff... maybe one of you knowledgeable guys want to update Wikipedia's definition of the cosmological event horizon: Its under http://en.wikipedia.org/wiki/Particle_horizon

Good suggestion. I would encourage SpaceT to give it a try.
I noticed that several of the Wiki entries in this department are self-declared "stubs" waiting for someone to contribute more informed extensive definitions that make clear what the differences are.

 

[Chronos]

Consider that this could be a mistake Chronos, because
the surface of last scattering is moving back away from us with lightning rapidity as it moves away, we have inside this sphere of last scattering always more and more of the universe, for us to observe and learn about, more and more galaxies, more and more regions of galaxy formation,

Illogical. It suggests light emitted by objects in front of the surface of last scattering travels slower than light from the CMB.

this statement is not true: " [i.e., we already see all of the... universe that will ever be possible to observe] "

A bold assertion, I believe it is a matter of opinion.

So far what I am saying makes no reference to neutrinos. I am talking about light.

A reflex action. I've been reminded a few times that the big bang is transparent to neutrinos nearly back to the Planck limit.

 

[SpaceTiger]

Illogical. It suggests light emitted by objects in front of the surface of last scattering travels slower than light from the CMB.

It's better to think of the "surface of last scattering" as a short period in the history of the universe rather than a static surface. As time goes on, the CMB light we see is coming from increasingly distant parts of the universe. At the time of decoupling, we would have seen CMB light all around us. Soon after decoupling, we would have been able to see light from objects very nearby, but anything beyond that would be "older" than the time of decoupling and would therefore be obscured. As the time since decoupling increases, more and more of the universe becomes visible, like marcus is saying.

 

[Chronos]

I just cannot wrap my head around that. I perceive the surface of last scattering [CMB] as an impenetrable wall - at least to photons. All other photon emitting objects must necessarily be in the foreground, IMO, hence their photons have already reached our observatory. I very much doubt we will ever detect any stars or galaxies beyond the CMB redshift [z~1100]. We will, however, see the evolution of foreground objects.

 

[marcus]

I just cannot wrap my head around that. I perceive the surface of last scattering [CMB] as an impenetrable wall...

I think this is a case where if you try just a little harder you will succeed in getting it: no problemo.

I like what SpaceT said. I had not thought of it that way but it makes it a lot clearer

It's better to think of the "surface of last scattering" as a short period in the history of the universe rather than a static surface.

Say that now the last scattering was 13 billion years ago.
And we wait for a billion years.
NOW the last-scattering epoch is FOURTEEN billion years ago.
So there is more of the universe, more galaxies, for us to look at and study, which are now between us and the epoch of lastscattering.

Essentially, "the wall has moved back".

... emitting objects must necessarily be in the foreground

there will be MORE UNIVERSE IN THE FOREGROUND in the future, for us to look at.

I very much doubt we will ever detect any stars or galaxies beyond... redshift [z~1100]...

In case you don't see what I mean, I will keep trying. the CMB will not ALWAYS have the redshift of z = 1100. when the CMB has a redshift of, say 1500, then nothing will in principle prevent us from studying proto galaxies or whatever curdling structure-formation crud that has redshift 1200. Or?

It may sound strange to you to think of the passage of a billion years and still have some kind of "us" observing the universe. But the context of the discussion is the mathematical limit of something as t -> oo.
If we take seriously the idea of making observation out to time infinity, as required by the mathematical definition, then we are obliged to imagine that something (maybe only a morose robot named Marvin, but SOMETHING) is still watchful and taking note, even after a long long time.

Anyway the main thing is that the "scatter-wall" is constantly moving back, exposing more and more of the universe to our quizzical gaze.

HTH.

 

[Chronos]

I agree the CMB will continue to recede over time. I do not agree any new objects will appear in the foreground, aside from those that evolve from objects already in view.

 

[SpaceTiger]

I agree the CMB will continue to recede over time. I do not agree any new objects will appear in the foreground, aside from those that evolve from objects already in view.

Nobody's saying that objects are popping out of nowhere. As I already said, new parts of the universe first become visible in the CMB. At this point, they don't contain galaxies or clusters, of course, but will if given enough time.

 

[Chronos]

I agree we will eventually observe the natural, albeit time delayed [redshifted], evolution of objects in the foreground of the CMB. What I do not foresee is hitherto unseen and evolved objects popping into view - or previously observed objects popping out of view.