From Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe: (link)

"We show that we can observe galaxies that have, and always have had, recession velocities greater than the speed of light. We explain why this does not violate special relativity and we link these concepts to observational tests."

The authors also wrote a less technical article based on the above paper, it is available in PDF form from the authors website: Misconceptions about the Big Bang

Basically, the scale factor of the universe was increasing very fast during its early stages. When the light from those high redshift galaxies in the Hubble Ultra Deep Field was emitted, nearly 13 billion years ago, they were only around 3.5 billion light-years away, but the region of space they were in was receding from this region of space at a rate faster than light. From our point of view, those photons were receding from us too and continued to recede for a long time.

But the rate of expansion was slowing, and eventually those photons found themselves in regions of space that were receding from here at a rate slower than light. Those photons crossed into our Hubble Sphere (which is the distance where an object that is moving with the expansion of the universe recedes at the speed of light) a little over 9 billion years ago, by which time they were passing galaxies that were 5.7 billion light years away from us!

Essentially, all the light we receive today, that has been travelling for more than 9 billion years, was emitted from regions that were had apparent recession speeds in excess of c, and this includes the Cosmic Microwave Background Radiation, which was emitted at an original distance of around 40 million light-years away, but took 13.7 billion years to reach us. Whatever is in a region of space where the CMBR we detect today was originally emitted from, if it has receded with the expansion of the universe, would today be something around 46 billion light years away.

The term "observable universe" is defined by the light we can see, as you say. There are many ways to measure it, depending on what you want to know. If you want to where things were when they emitted the light we see, you get one answer, known as the angular diameter distance. If you want to know an approximation of where everything is "now", you get another answer, known as the comoving radial distance. If you want to know how long ago the light was emitted, you get yet another answer, known as the light-travel or lookback time.

Have a look at this page from the atlas of the universe:

The Distance Scale of the Universe. (note: this page uses slight old figures that are now considered a little high)

I have no quarrel with the superluminal speeds of the universe, nor with how long it took for the light to reach us. While it’s true that you can ask different questions and get different answers for each question, some times the answers given or the things stated, are just plain wrong.

True - We can glimpse a galaxy from 13 billion years into the past.

True - That galaxy is now 30 billion light years away in true time.

False - So we can now see 30 to 38 billion light years away, and that is our observable universe.  i.e. If I show you a stone, and then I throw it into some bushes and trees, would you say that it is still observable? 

True - We cannot see that galaxy as it is today, and we will never be able to see it, as it is now receding from us at over twice the speed of light. It is not observable.

True - Our observable universe can only go back as far as when the universe began. Only about 13+ billion years ago. Let’s stick to what "observable" truly means.

 Quite correct. So how large is the observable universe? If we take the angular diameter distance, which seems to be your favored choice, then the universe has an observed radius of 5.7 billion light-years. The objects we have observed as having the largest angular diameter distances are those that were at the edge of our Hubble Sphere, 9.1 billion years ago. All older light, that has been travelling for longer than 9.1 billion years, was emitted at an original distance of less than 5.7 billion light-years.

So, your observable universe, where everything is where it was when it emitted the light we now see, has a radius of 5.7 billion light years, which equates to light-travel time of 9.1 billion years and a redshift of around z=1.4. We have seen far more "distant" (in time) objects, with redshifts of up to z=7 or so, but they were nearer to us when they emitted their light, only around 3.5 billion light-years away as the universe was smaller at that time. The CMBR has a redshift of z=1089 and those CMBR photons we detect today were emitted a mere 40 million light-years away, 13.7 billion years ago.

That's your observable universe, defined by what we observed, and where we think it was when the light we observe was emitted. The photons that have been travelling the longest were originally emitted the closest, and the photons emitted around 4.5 billion years after the Big Bang were the ones that were emitted at the highest distance.

SpeedFreek:

So how large is the observable universe?

Would you care to comment on the "great attractor"?

Dusty_Matter:

The question “how large is our observable universe” is not answerable in terms of distance, but it is answerable in terms of "time". The further out in distance we look, the further back in time that we see. The furthest we can observe is roughly back to about 13 billion years ago.

The look-back time is the most useful, but what use is it on its own? We can see these galaxies, and the galaxies with the highest look-back times (z=7 or 13 billion years) were much closer to this region of space when their light was emitted than a galaxy at z=1.4 was (9.1 billion years). The z=1.4 galaxy had nearly twice the proper distance at the time of emission.

How can we assign a coordinate in space-time if we only use time?

Dusty_Matter:

Again it’s not, “where we think it was when the light we observed was emitted” but when we think the light we observed was emitted.The galaxy we observe from 13 billion years ago, is not observable in our present time, from where it is calculated to be now. Our observable universe goes to only about 13+ billion years into the past, and that is the farthest we can see.

Dusty_Matter:

Would you care to comment on the "great attractor"?

I would have to see the quote you are referring to.

Dusty_Matter:

True - We can glimpse a galaxy from 13 billion years into the past.

True - That galaxy is now 30 billion light years away in true time.

And here we have the essence of two distance measures, one "observed", and one inferred from what we have observed, but referred to as "true time"?

When we say we have observed that the light is 13 billion years old, we are talking about the redshift, from which we infer the light travel time! The basis of this inference is that the universe is expanding, which causes the redshift. So in order to establish the lookback time from the redshift, we also generate the comoving distance at the same time, it falls out of the same equations.

One is just as "real" as the other.

Dusty_Matter:

The question remains one of observation. If it is answerable in terms of distance, then please, you tell us how big our observable universe is. How far can we observe? Not how far are the objects now.  Can you give us a specific distance?

Yes I can give you a specific distance, and I have done so already. We have seen out to a distance of 5.7 billion light-years, the Hubble distance as we see it. Not where it is thought to be "now" (around 14 billion light-years), but where it was "then".

Dusty_Matter:

The commoving radial distance is good for anything nearby but becomes more difficult with distance.  Again, can you give us a specific outer visual distance for our observable universe?

Why do you say comoving radial distance is good for anything "nearby"? We see everything at the distance it was when the light was emitted. Why is it any better to say a nearby galaxy with a redshift of z=0.1, whose light was emitted only 1.28 billion years ago, was originally only 1.22 billion light-years away but is now 1.35 billion light-years away? How is that any more "real" than saying a z=7 galaxy was 3.5 billion light-years away but is now 28 billion light-years distant?

Dusty_Matter:

I agree that you do need spatial dimensions to build a meaningful model, but that was not part of the question. How far can you actually see, not infer, is how I see the question, and how most people would ask it.

Dusty_Matter:

Yes, the commoving distance does come out of look back times from the red shift, but can you actually observe them as they are now in our present time?

No, of course we cannot see those galaxies where they are now. The maximum proper distance we have seen is 5.7 billion light-years, and what we see there are galaxies that were receding at the speed of light when they emitted the light we see. That light was emitted 9.1 billion years ago. That is the edge of our Hubble Sphere as we see it, and it is often referred to as the visible universe.

Our observable universe, on the other hand, is defined by the Cosmic Microwave Background Radiation, its emission distance (the CMBR photons we currently detect were originally emitted only 42 million light-years away, in all directions), and the distance that the emission coordinates would have receded if they were comoving with the expansion of the universe (46.5 billion light-years), which is known as the particle horizon.

What you are looking for, is the observed or visible universe, not the "observable" universe, which is a cosmological definition, based in general relativity. The observable universe considers the history of the space-time from which we have received information. It is only observable theoretically, using the mathematics of the Lambda-CDM concordance model. Unfortunately, a lot of mainstream media articles are not very good at explaining this properly.

Dusty_Matter:

The observable universe (according to wikipedia) consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because the signals from those objects has had time to reach us…

This contradicts your definition. The signals or light from the galaxies and other matter that is inferred to be 30+ billion light years away cannot be observed in the present day on Earth because their signals have not reached us, and they never will.

This is the meaning of the term observable that most people are referring to, and this is the definition that I am referring to.

The further away that we view an object, the older our visual information is, and the greater our discrepancy with a commoving radial distance reading. (What we see doesn’t match it’s actual location.)

It comes down to not actually seeing it’s location in space, but actually it’s location in time.

So if you want to stick to our visual distance as being 5.7 billion light years. So be it.

If others want to say that our observable universe is 30+ billion light years in distance. They are misleading, and in my opinion wrong.

Our observable universe goes to about 13+billion years into the past, and that’s how far we can see.

Thank you for such a lively discussion though Speed Freek. It was very invigorating, and I did learn a few things. I hope others did too.

It may be the definition that you are referring to, but it is not the definition used in science. You will notice that the wiki article also says "The age of the universe is about 13.7 billion years, but due to the expansion of space we are now observing objects that are now considerably farther away than a static 13.7 billion light-years distance. The edge of the observable universe is now located about 46.5 billion light-years away." In fact, the article does not contradict me at all.

SpeedFreek:

No, of course we cannot see those galaxies where they are now.

Dusty_Matter:

I maintain that the time definition for how big is our observable universe is, is the most accurate statement for how large the observable universe is.

So, you can understand how large it is by knowing how old it is? Our observable universe has a radius of 13.7 billion years then. But what does that actually mean, in terms of how big, or how large, it is?

Nobody is saying we can see the edge of the observable universe as it is today. We can see the edge, as it was 13.7 billion years ago (the CMBR), and its redshift (derived using WMAP) tells us how much the universe has "stretched" since. The redshift tells how the scale of the universe has changed between the emission of that light and our detection of it. The CMBR has a redshift of z=1089, which means the universe is 1090 times larger "now" (1+z), than it was "then". The place where that light was emitted from is now 1090 times further away than it was. 42 million light-years has turned into 46 billion light-years.

Earlier, I said that the observable universe can be defined as the history of the space-time from which we have received information. We have seen information from these regions of the universe, and the redshift/luminosity/surface brightness information tells us how long ago the light was emitted, where the light was emitted, and how much the universe has expanded since. All these measurements are on an equal footing as all are derived from the same information, using the same mathematics.

If the universe were not expanding, putting more distance between the source and the eventual detector of light, there would be no cosmological redshift. By accepting that cosmological redshift tells us how long the light has been travelling, you are accepting that the universe has expanded during that journey, and that the emitter of that light is now further away than it was.

Basically, cosmologists like to take what the astronomers have seen and analyse it using the best cosmological theory we have, to understand the evolution of the universe from what it was to begin with to what it is today, and it has been given the term "the observable universe" as it is based on the region of the universe to which we have been connected by photons.

SpeedFreek:

So, you can understand how large it is by knowing how old it is?

Dusty_Matter:

SpeedFreek:

So, you can understand how large it is by knowing how old it is?

 

No. I have not been talking about it’s size, nor can that connection be made.

SpeedFreek:

Our observable universe has a radius of 13.7 billion years then. But what does that actually mean, in terms of how big, or how large, it is?

You seem better adapt at answering that question. I was not making a comment on how big or large it is. That is a different topic. I was only commenting on what is observable.

Well I must have misunderstood you then, when you said:

Dusty_Matter:

I maintain that the time definition for how big is our observable universe is, is the most accurate statement for how large the observable universe is.

What do you mean when you use time to define how big, or how large, the observable universe is?

Dusty_Matter:

SpeedFreek:

Nobody is saying we can see the edge of the observable universe as it is today.

Then why say that we can see 30 to 40 billion light years away? If it is not true, then people shouldn’t be saying that.

Nobody is saying that we can see 30 to 40 billion light years away! What we say is that the most distant parts of the universe that we have seen are "now" up to 46 billion light-years away, but we are not saying we have seen across a distance of 46 billion light-years.

Dusty_Matter:

I guess another way of looking at it would be akin to the event horizon of a Black Hole.

It has been claimed that we have seen our own central galactic black hole swallow up a star that was once in orbit about it. Yet no one claims to be able to observe what happened to this star beyond the event horizon of our black hole, the point at which photons are no longer in contact with us.

The expansion of our universe at great distances does in essence the same thing. We are cut off due to time, speed of recession, and distance, to objects that we are viewing as having existed 13 billion years ago. So why claim that they are observable to us today beyond this obvious barrier beyond which, we will never see them again?

Nobody claims they are observable to us today beyond that barrier, you have misunderstood the scientific meaning of the term "the observable universe", which I admit has a definition that is somewhat counter-intuitive. But as you look deeper into this subject, you find that all the distance measures are required to comprehend the evolution of the universe.

Let me give you an example to show you why all three distance measures have to be considered.

Lets look out into the universe and describe what we see at further and further "distances", using the three distance measures.

Light-travel time.

z=0.1 - a galaxy whose light is 1.2 billion years old.

z=1.4 - a galaxy whose light is 9.1 billion years old.

z=7 - a galaxy whose light is 13 billion years old

z=1089 - the CMBR, which is 13.7 billion years old.

Angular diameter distance.

z=0.1 - a galaxy that was 1.2 billion light-years away

z=1.4 - a galaxy that was 5.7 billion light-years away

z=7 - a galaxy that was 3.5 billion light-years away

z=1089 - a CMBR photon that was emitted 40 million light-years away.

Comoving distance.

z=0.1 - a galaxy that has receded to 1.35 billion light-years away.

z=1.4 - a galaxy that has receded to 13.7 billion light-years away.

z=7 - a galaxy that has receded to 29 billion light-years away.

z=1089 - a CMBR photon whose emission point has receded to 46.5 billion light-years away.

The angular diameter is what is actually seen. The dimmest, most redshifted galaxies look larger in the sky than brighter, less redshifted galaxies. It is only when the redshift drops below z=1.4 that galaxies look closer in distance as they get closer in time. Above that redshift, galaxies look closer in distance as they get further away in time! This is because they were closer to us, as the universe gets smaller and smaller, the further back in time we look.

For a z=7 galaxy to look a lot closer than a z=1.4 galaxy makes no sense if you simply use the redshift as an indicator of the age of the universe without also considering where the z=7 galaxy must have receded to by the time its light finally passed that z=1.4 galaxy. When the z=7 galaxy emitted the light we see, the z=1.4 galaxy (or whatever was in that region of space at that time) was a lot closer to us than the z=7 galaxy. When the z=1.4 galaxy emitted the light we see, the z=7 galaxy (or whatever was in that region of space by then) must have been a lot further away than the z=1.4 galaxy.

I know you argue that we shouldn't apply the term "observable" to the universe as we think it is today, but that term has been chosen. It differentiates the parts of the universe that we have seen from the parts we have never seen, and it accepts that all the parts are becoming more distant from each other.

We have received light from a region of space that is now 46 billion light-years away, but that region was a lot closer when the light was emitted. For all we know the whole universe might only have a radius of 50 billion light-years (or it might even be infinite!), but we think the parts we have seen are currently not less than 46 billion light-years in radius.

SpeedFreek:

What do you mean when you use time to define how big, or how large, the observable universe is?

Dusty_Matter:

SpeedFreek:

Any "speculation" about the current size of the observable universe is as valid as any "speculation" on the current age of the observable universe. We cannot see the passage of time...

I totally disagree with you there. The size of the universe is unknown. The age of the universe has now been pegged down pretty precisly from what I’ve heard and read.

I said the size of the observable universe! (which has been pegged down just as much as the age of the universe, as it falls out of the same equations) 

Dusty_Matter:

So what you’re saying in essence by saying that the universe might only have a radius of 50 billion light years, is that, what we’ve seen so far, might just about be all there is to our universe? If that is possibly the case, then what is there really for sure to differentiate from?

There is stuff that we have seen, there is stuff that we can no longer see, and then there might be stuff that we have never seen? It doesn’t seem to me that the way they have chosen to use the word observable really differentiates anything concrete at all. It also seems to me that, whoever chose the to use the word “observable” in this fashion, really didn’t understand what he was doing in the first place.

However as you say, “… that term has been chosen.” and I know that I cannot change that. I can only resolve myself not use that term in that manner, because I think it is wrong.