Position of Earth in the Universe

[Born2Perform]

After Hubble studies all are according about space expansion;

I heard many times expert people on this forum conclude that the Earth must be quite near the center of it, in order that our view is isotropic and 10/11 galaxies are moving away from us.

I think this is a non-sense: think for a second what would be the situation if we would be about at the edge of the universe: the same. galaxies near the center would appear to us moving with growing speed in time.
We cannot say we are accelerating in order that space itself is expanding and we are firm, so symmetry principle is still valid..

my english is disastrous but...isn't right that Earth could be at almost every position in universe?

 

[Garth]

Yes, the universe is thought to be homogeneous, the CMB is certainly isotropic to a high degree of accuracy (to within one part in 10⁵), so the Earth could be almost anywhere within it and the view on the largest scales would be pretty much the same as from here.

The universe does not have an 'edge' nor 'centre', just as the Earth's surface does not have an edge or centre.

Garth

 

[SpaceTiger]

I heard many times expert people on this forum conclude that the Earth must be quite near the center of it, in order that our view is isotropic and 10/11 galaxies are moving away from us.

Either those people weren't experts or you misunderstood what they were saying. It has been said several times that the Earth is at the center of the observable universe, but the observable universe is just all that we can see, not all that there is. It should be no surprise that we're at the center of a region defined by all that we can see.

 

[Chaos' lil bro Order]

lol@ST funny last sentence.

 

[VikingF]

If the universe is infinite, then asking where Earth is, is like asking where on the x-axis we'll find x=3.

 

[Jenny]

Homogenous universe:
To tie in expansion:
Have you heard of the rubber band 2D analogy of expansion?
Imagine that we rre a dot on a rubber band and there are numerous dots on the rubber band with similar spacing between each dot. the rubber band is expanding, we would see every dot moving away from us and further dots moving faster (because it's the space between EACH dots getting larger AT THE SAME RATE, but from one DOT, the further the dot we are looking at, the faster it is moving away.)
This analogy applies to the universe, except the rubber band is a 1D figure expanding in 3D space. We can have a 2D figure expanding in 3D space if we imagine a rubber balloon expanding- it similarly has equally spaced dots on it)

What Garth said is right: "The universe does not have an 'edge' nor 'centre', just as the Earth's surface does not have an edge or centre."
The Earth's surface, ie. 2D space, doesn't have an edge or centre, if you think that the centre is the core, well, that's in 3D space...(I just said that because I think it's important to realize that the analogy of the Earth is GREAT except when we try to imagine a universe with it's 3D space... it's not existing in an extra dimension, so hard to visualise!.. in fact, impossible- or is it? hehe, somebody tell me)

 

[Jorrie]

... It has been said several times that the Earth is at the center of the observable universe, but the observable universe is just all that we can see, not all that there is. It should be no surprise that we're at the center of a region defined by all that we can see.

Always useful to remind people that we are at the center of our observable universe just like a sailor on the open sea is at the center of his observable ocean. There is no edge there, just a horizon.

 

[oldman]

Always useful to remind people that we are at the center of our observable universe just like a sailor on the open sea is at the center of his observable ocean. There is no edge there, just a horizon.

I fear that when folk (Space Tiger and yourself in this case) imply like this that there is something beyond the observable universe they are elevating an assumption that we can never verify to the status of an accepted fact.

This takes us into the territory of space-operas that invoke galactic empires, bug-eyed monsters, black holes and time warps whenever they are set beyond the now-familiar territory of the solar system; we've always found it convenient to relegate unexplained mysteries to far-away places, or to the distant past or future, where they entertain us but can't threaten us.

Extrapolation beyond the red horizon/edge? of the observable universe is rather reminiscent of the old practice of talking up demons, deities, spirits, sea-serpents, and dragons, or the new habit of speculating about bubble universes.

Isn't the standard model, with its inflationary scenario, speculative enough already?

 

[marcus]

Hi oldman,

I want to make the point that in the LambdaCDM model there is indeed a "cosmological horizon"-----a kind of limit to how much the observable universe can, in principle, encompass even if one waits 100s of billions of years.

but that is not what one means by "observable universe". Observable means the galaxies and stuff that is ALREADY observable----with light and particles we are already receiving. That is what they conventionally mean by it, and THAT is steadily enlarging. As time goes on we get light from more and more galaxies.

I fear that when folk (Space Tiger and yourself in this case) imply like this that there is something beyond the observable universe they are elevating an assumption that we can never verify[/color] to the status of an accepted fact.

...

Extrapolation beyond the red horizon/edge? of the observable universe is rather reminiscent of... the new habit of speculating about bubble universes.
...

For me it is not reminiscent. I am not interested in the "bubbles" of eternal inflation or all that Susskind stuff. But the gradual enlargement of the up-till-now observable universe is for me a humdrum straightforward assumption----nothing like "multiverses" and bubble speculation.

you express your idea in an entertaining and persuasive way, but I think it involves an error (see red)

I will associate myself with Jorrie and SpaceTiger in accepting the assumption that there is plenty of universe beyond the edge of what we have so far observed, and we will eventually be able to observe it.

call this a prediction or an assumption, as you chose. it is in principle verifiable and it is totally unimaginative (not like your "dragons")

I assume that the edge of what we have (up to the present) observed steadily moves outwards from us and, if one is very patient (extremely patient ) one can OBSERVE it to do so.

I assume the region from which light and neutrinos etc. have so far reached us (conventionally called the observable universe) is continually enlarged so as to contain more and more galaxies

Note that I am not talking about the Albertesque expansion of space but the increase in the number of galaxies which we are in principle able to observe. the simple arrival of more data.

I assume this because it is the simplest. One does not have to invent anything. The least complicated cosmological model fitting the data predicts that (very long term ) we will notice that more and more galaxies are in the observable universe.

To put it in concrete operational terms (so that you can "swing your cat"), the simplest model predicts that some day the redshift of the last scattering (the CMB) will be not 1100, but 1200. and then the temperature of the CMB will be not 2.75 kelvin, but more like 2.50 kelvin.
And within that enlarged sphere, enclosed by a more distant last scattering surface, there will be more galaxies---for our decendents or replacements to count and study, if Life in that future time is still curious about the world.

Assuming as I do is, imo, NOT SPECULATIVE. One takes the simplest model that fits----one checks it as well as one can against all available data---this enlargment is what it predicts----ONE CAN IN PRINCIPLE VERIFY although it will take a long time. And for this enlargment NOT to happen would be very surprising and awkward. One would have to rebuild the model probably in some ugly way, to accommodate the idea that the enlargement of what can so far be observed should abruptly halt---with no more galaxies coming in over the horizon as it shifts outward.
============

BTW just as a footnote. the CMB was originally only some 3000 kelvin. there is lots of hotter stuff in galaxies that one can see (like Xray, gamma).
so at some time in future I suppose people will "see" galaxies at 1100 but brighter and clearer than they now see CMB at 1100---because hotter.
and then neutrinos do not redshift, so that's another means to see deeper

 

[marcus]

oldman,
maybe you would like this

http://arxiv.org/astro-ph/0605709


it is by Scott and Ziblin. I think it may have been SpaceT who told me about this article.

using the current WMAP data, and what they regard as the simplest cosmological model(s), they calculat that

THE REST OF THE UNIVERSE MUST BE AT LEAST 10 TIMES THE VOLUME of the observable universe.

Of course it could be infinitely larger, or it could be finite but 1000s of times larger. But they use the observations of flatness to conclude that the real volume is AT LEAST tenfold larger than the volume of the observable universe.

 

[Jenny]

sorry to pick out such a small part of your discussion.. but I'm a little confused

neutrinos do not redshift, so that's another means to see deeper

Redshift used in that sense is the lenghtening of all wavelengths. However, neutrinos are particles without wave properties (right?) so obviously they don't redshift in that sense. However, if neutrinos from a source that is emitting neutrinos for 3 seconds, from a region of space where there is a large cosmological redshift (ie. very far away) the observer here on Earth would see an affect due to large 'redshift' or distance. The source would be seen to be emitting neutrinos for longer than 3 seconds. This is the slowing down of time in the past. (you can look it up online probably for an explination)
What I don't get Marcus, is why does neutrinos not redshifting mean that we can look deeper with it?
{i'm not arguing that neutrinos don't offer a method of observing an earlier universe (theoretically, but not practically at the moment) than electromagnetic radiation. But the reason for that isn't because it doesn't redshift in the conventional way is it? It's because the universe became transparent to neutrinos earlier than electromagnetic radiation. "In general, the weaker the interaction of a particle with matter and radiation, the further back in time it can come from without having been scattered or blocked."
Ref: Swarup, A 2006, “Ghostly particles carry imprint of early cosmos”, New Scientist, 10 April 2006, p18}

 

[oldman]

I think it involves an error (see red)... I will associate myself with Jorrie and SpaceTiger in accepting the assumption that there is plenty of universe beyond the edge of what we have so far observed, and we will eventually be able to observe it... I assume that the edge of what we have (up to the present) observed steadily moves outwards from us and, if one is very patient (extremely patient ) one can OBSERVE it to do so.

Thanks, Marcus. Yes, it was indeed an error to say "never", and you are right about things changing. I can only plead oversimplification of what has for some time struck me as a quite complicated situation -- see below.

Consider horizons:

First, there is a boundary which limits our experience, which I’ll call
the Horizon. By this dictionary definition, we can only speculate about happenings concerning objects (that I'll call events) beyond this boundary, at least until the situation changes as you describe.

Second, there is a working horizon, beyond which our instruments are not yet sophisticated enough to penetrate. Our working horizon varies
with the kinds of objects studied and the wavelength of radiation they
emit, and may be changed by invention. At infrared, optical and X-ray
wavelengths it now lies among remote galaxies with active centres, whose light is strongly reddened. At longer wavelengths the working horizon is the cosmic microwave background which presently serves as our Horizon.

In cosmology there are also two kinds of intangible boundaries that have the potential to be our Horizon. These boundaries depend on the nature and history of the universe, and especially on general relativity.

A “big” (as compact as you like but perhaps infinite, with a finite scale factor) universe, which somehow suddenly “began”, contains ourparticle horizon, beyond which light has not had time to travel to us since the universe began. The particle horizon defines the limit of communication and hence the maximum size of isothermal regions. Our working horizon and our Horizon cannot be further away than the particle horizon. In such a “big” universe, as time passes, the particle horizon dilates away from us at the speed of light, bringing previously unobservable events into our ken as time passes.

That is why I shouldn't have said "never". But there is more:

In a “big” enough universe, which is expanding rapidly enough, there
will be a boundary beyond which events expand away from us at
"speeds" faster than light (allowed by general relativistic expansion).
This is our event horizon. Its size depend on the rate of expansion. In the fullness of time the particle horizon may, as it dilates, reach the
event horizon. It cannot dilate further, since the event horizon
may then limit our experience and become our Horizon. One expects light from near the event horizon to be reddened by general relativistic expansion near light speeds.

Observation shows: (1) that our working horizon is red, from which
we conclude that it is close to our event horizon and (2) that on opposite
sides of the sky our red working horizon looks the same. This is to be
expected iff the distance to the particle horizon for all observers is the
same (Copernican principle) and about twice the distance to both our
working horizon and the nearby event horizon.

But the distance to the particle horizon cannot be greater than that to the event horizon.

This unsatisfactory situation is known as the "horizon problem of the
standard model".

The inflationary scenario resolves the difficulty by manipulating the
position of the event horizon with a changing rate of expansion. With
suitably chosen parameters (the number of e-fold expansions, the
duration of inflation and the rate of ordinary expansion before and
after inflation) inflation temporarily reduces the size of the event
horizon, which, as it shrinks, gathers up the particle horizon, as it were, and moves it back into a part of the universe which has already reached thermal equilibrium.

As inflation ends the event horizon gets biggers as the expansion rate slows, but leaves behind in the early universe a relic in the form of a particle horizon around only part of an isothermal region. During the subsequent ordinary expansion this particle horizon dilates and sweeps over some, but not all, of the events in the expanding isothermal relic of the primeval universe.

The net result is that our present horizon can come to enclose only part of the pre-inflation isothermal universe. The horizon problem is thus resolved, or should I say finessed?

My trouble is really with the inflationary scenario, that involves speculation about a primordial universe now beyond our Horizon. But I suppose I'm being too old-fashioned.

 

[SpaceTiger]

Extrapolation beyond the red horizon/edge? of the observable universe is rather reminiscent of the old practice of talking up demons, deities, spirits, sea-serpents, and dragons, or the new habit of speculating about bubble universes.

There are many astronomers (usually observers) who would agree that we should only discuss the observable universe. However, I'm not one of them, and I have several reasons.

First is the inflationary scenario, which has been and will continue to be tested observationally. Although it does not require a universe of size bigger than we observe, it does allow for it just as naturally as a universe that is smaller. Observations of the microwave background rule out a universe of size much smaller than our particle horizon, so the majority of what remains of parameter space leaves much that we don't see.

Second is the Copernican principle. The size of the observable universe has grown many times over since the end of inflation. The cosmic microwave background, at z~1100, contains some 40,000 observable regions that could not observe one another at the time of decoupling. If the universe had a topological scale around the size of our particle horizon, that would suggest that we are somehow special and the observable universe has stopped growing just in time for our appearance. Traditionallly, astronomers have tried to avoid theories that put humans in a special place because nature is, for the most part, not sensitive to our existence. Rather, such theories usually arise as a result of our hubris.

Finally, although these other parts of the universe are not currently observable, they may have been in causal contact with our part of the universe prior to inflation. As such, they should not be neglected from a theory of our origins.

I'm not saying that we're sure the universe is larger than we can observe, I just think it's important to keep it in the discussion. Like marcus, I think your comparison to dragons, demons, etc. is unwarranted.

 

[marcus]

{i'm not arguing that neutrinos don't offer a method of observing an earlier universe (theoretically, but not practically at the moment) than electromagnetic radiation. But the reason for that isn't because it doesn't redshift in the conventional way is it? It's because the universe became transparent to neutrinos earlier than electromagnetic radiation...

good point Jenny! what I said was careless.
I agree with what you said that I bolded.

it might be that their not losing energy as space expands will ALSO contribute to the usefulness of neutrinos as a probe into early universe, but I believe their primary advantage is what you said.

===============
incidentally what i was talking about was not really the present situation of observational cosmology but the far distant future when galaxies are seen at z = 1100, instead of just 6 or 7 like now:

BTW just as a footnote. the CMB was originally only some 3000 kelvin. there is lots of hotter stuff in galaxies that one can see (like Xray, gamma).
so at some time in future I suppose people will "see" galaxies at 1100 but brighter and clearer than they now see CMB at 1100---because hotter.
and then neutrinos do not redshift, so that's another means to see deeper

the problem I imagine facing observational astronomy way in the future is that ordinary visible light will become feeble long wavelength stuff offering poor resolution----microwaves don't give such a great image. so astronomers may find themselves relying more on light that was originally emitted as Xray or gamma----or even (as I meant to say) not even on light at all, but particles like neutrinos.

I didnt mean to suggest that right NOW the primary attraction of neutrinos is that they don't redshift, I meant that in a hypothetical future context where ordinary light from the most distant galaxies has been redshifted to near uselessness

 

[Chaos' lil bro Order]

.

Finally, although these other parts of the universe are not currently observable, they may have been in causal contact with our part of the universe prior to inflation. As such, they should not be neglected from a theory of our origins.
.

Great post ST, I thoroughly enjoyed it. Does inflation theory have observational evidence, or is it a theory born out of necessity used to solve the horizon problem? I suspect it doesn't show in the WMAP because WMAP surveyed the 370,000 year old CMB and inflation occurred in the first fractions of second.

 

[Jorrie]

...
To put it in concrete operational terms (so that you can "swing your cat"), the simplest model predicts that some day the redshift of the last scattering (the CMB) will be not 1100, but 1200. and then the temperature of the CMB will be not 2.75 kelvin, but more like 2.50 kelvin.
And within that enlarged sphere, enclosed by a more distant last scattering surface, there will be more galaxies---for our descendents or replacements to count and study, if Life in that future time is still curious about the world.

Thanks for a great post marcus! One thing that puzzles me in what you said in the quoted portion above: I understand that as time goes on, we can see further in light-travel-time. But, due to the accelerating lambdaCDM expansion, will some of those present farthest galaxies not move out of our then (larger) observable universe?

 

[oldman]

Second is the Copernican principle. The size of the observable universe has grown many times over since the end of inflation. The cosmic microwave background, at z~1100, contains some 40,000 observable regions that could not observe one another at the time of decoupling. If the universe had a topological scale around the size of our particle horizon, that would suggest that we are somehow special and the observable universe has stopped growing just in time for our appearance. Traditionallly, astronomers have tried to avoid theories that put humans in a special place because nature is, for the most part, not sensitive to our existence. Rather, such theories usually arise as a result of our hubris.

I'm persuaded by most of what you say in your reasonable post.

I wasn't aware that the horizon problem is so exacerbated by the uniformity (I presume) of the cosmic microwave background. Thanks for pointing this out. It certainly emphasizes the need for a solution to this difficulty, like inflation.

You also said: "If the universe had a topological scale around the size of our particle horizon, that would suggest that we are somehow special and the observable universe has stopped growing just in time for our appearance" . I'm not clear what you mean by "topological scale". Do you mean the separation of places where the universe might connect on to itself, as if it were closed or multiply connected in some fashion?

I thought one of the less appealing features of inflation was that it did away with the Copernican Principle, in that it solved the horizon problem by assigning to us a special location somewhere in the central regions of an relic isothermal patch of the primeval chaos. You seem to be saying the opposite; namely that an appealing feature of inflation is that it supports the CP. I am muddled by how this can be.

 

[SpaceTiger]

Do you mean the separation of places where the universe might connect on to itself, as if it were closed or multiply connected in some fashion?

That's right.

I thought one of the less appealing features of inflation was that it did away with the Copernican Principle, in that it solved the horizon problem by assigning to us a special location somewhere in the central regions of an relic isothermal patch of the primeval chaos. You seem to be saying the opposite; namely that an appealing feature of inflation is that it supports the CP. I am muddled by how this can be.

The first two points are separate. I'm saying that the Copernican Principle can be used to support the idea that the universe is larger than our particle horizon if the observable universe has grown many times over since the epoch of recombination, or earlier (after the end of inflation in the standard model). This is not the same as saying that the Copernican Principle can be used to support inflation over other theories of the early universe.

 

[SpaceTiger]

Great post ST, I thoroughly enjoyed it. Does inflation theory have observational evidence, or is it a theory born out of necessity used to solve the horizon problem?

Both. See the https://www.physicsforums.com/showthread.php?t=114527".

 

[SpaceTiger]

But, due to the accelerating lambdaCDM expansion, will some of those present farthest galaxies not move out of our then (larger) observable universe?

You're right, in fact, but to be part of our observable universe, we only need to be able to see them at some point in their history. If the universe accelerates to the point where these galaxies are expanding away from us at faster than the speed of light, then their evolution after that time will never be observable to us. However, there will still be light traveling to us from these galaxies that was emitted earlier in their history. As time approaches infinity, we'll see the light that was emitted from them just before they began receding at faster than the speed of light. Of course, this light will be redshifted to the point of being unobservable, but in theory, it will be there.

 

[oldman]

http://arxiv.org/astro-ph/0605709 ... is by Scott and Ziblin...using the current WMAP data, and what they regard as the simplest cosmological model(s), they calculat that

THE REST OF THE UNIVERSE MUST BE AT LEAST 10 TIMES THE VOLUME of the observable universe.

Thanks for this reference, Marcus.

I see that Scott and Ziblin also calculate that the "apparent particle horizon" is about 3.5 times as far as the Hubble radius. But the Hubble radius is where the recession velocity extrapolates to c and is (close to?)the radius of the event horizon. Now whichever cosmological horizon is closest to us, is our actual Horizon -- the one that in fact limits our experience ---see my post #12 in this forum. There can only be one experience-limiting boundary.

Ipso facto, we can have no way of telling if what is beyond the Horizon of this epoch is more universe, or shoals of sea serpents. We may believe in a bigger universe, and indeed it is a lot more reasonable than sea serpents. But we can't be sure, and must categorise such extrapolations as speculation.

I maintain that in a speculative subject like cosmology one should clearly distinguish between such activities and things we can hope to someday disprove or verify.

 

[SpaceTiger]

I see that Scott and Ziblin also calculate that the "apparent particle horizon" is about 3.5 times as far as the Hubble radius. But the Hubble radius is where the recession velocity extrapolates to c and is (close to?)the radius of the event horizon. Now whichever cosmological horizon is closest to us, is our actual Horizon -- the one that in fact limits our experience ---see my post #12 in this forum. There can only be one experience-limiting boundary.

The particle horizon is the experience-limiting boundary. The Hubble radius is not an actual horizon (just a scale distance) and the event horizon is the maximum comoving distance that can be causally influenced by us in the future.

I maintain that in a speculative subject like cosmology one should clearly distinguish between such activities and things we can hope to someday disprove or verify.

How can we know what will and won't be someday verifiable. I think it's best to leave the theoretical possibilities open and not try to force our own limitations on the universe itself.

 

[marcus]

... But the Hubble radius is where the recession velocity extrapolates to c and is (close to?)the radius of the event horizon. Now whichever cosmological horizon is closest to us, is our actual Horizon -- the one that in fact limits our experience ---see my post #12 in this forum. There can only be one experience-limiting boundary.
...

Hi oldman, I would guess from your post that you believe that if a galaxy is NOW receding faster than c, then no matter how long we wait we will never receive the light that it is emitting in our direction NOW.

If you believe this, please affirm. I happen to disagree and will try to persuade you to my viewpoint. (Many people seem to believe this.)

Many people also seem to believe that it would be impossible for us to be receiving light NOW which was emitted by a galaxy back THEN at a time when the the galaxy was receding from us at speed greater than c.

Please say if you think this. As I understand it, this is a misconception based on misunderstanding the physics. You may also possibly have this (in-my-view) misconception----it is a translation back in time of the situation I described earlier. If so, I will try to convince you otherwise.

I will illustrate this with an hypothetical example of a galaxy whose light we are receiving now, which light was emitted when the recession speed of the galaxy was 2c.

 

[marcus]

yes, in case anybody has the misconception which I imputed to oldman (not actually knowing if he believes it himself or not)

here is an example.

take this calculator
http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html

put in omega (matter) = .27
lambda (dark energy) = .73
present Hubble parameter = 71
redshift z = 4

then you will see that any galaxy we observe with redshift z
was receding from us at speed 2.03 c (over twice the speed of light)
at the moment when it emitted the light which is arriving here today.

and any galaxy with redshift MORE than 4, you can easily check, was receding from us at MORE than twice c, when it emitted the light which we are now receiving from it.

the essential reason is that over the course of history the Hubble parameter has decreased, and so the Hubble radius has increased (reaching out and encompassing light which might have thought it had no chance to reach us ). in earlier times the Hubble radius has grown extremely fast.

the dynamic shrinking of the Hubble parameter is governed by a differential equation called the Friedmann equation---key to a lot of standard cosmology physics. the calculator here is based on the standard (Friedmann) model----all it does is "solve the differential equation" for you.

 

[SpaceTiger]

Hi oldman, I would guess from your post that you believe that if a galaxy is NOW receding faster than c, then no matter how long we wait we will never receive the light that it is emitting in our direction NOW.

If he did believe this, then he would be correct, at least in the asymptotic \Lambda CDM. The expansion is now accelerating, so the Hubble sphere is getting closer. In order to see galaxies (as they are now) that are now receding at greater than c, the expansion would have to decelerate in the future. This is possible, but is not in the standard model.

Either way, though, the Hubble radius is still not the same as the particle horizon and does not define the size of the observable universe.

 

[marcus]

... at least in \Lambda CDM. The expansion is now accelerating, so the Hubble sphere is getting closer...

I don't like to disagree, and this could be considered a minor point. I was under the impression that if one one limits one's view to the standard picture---Lambda CDM---then indeed expansion is accelerating. And all that means is that ä(t) is positive: the second time-derivative of the scale param is positive. AFAIK it does not necessarily mean that the Hubble parameter is increasing (so that the radius is diminishing and the sphere is getting closer)

So I was under the impression that this does NOT necessarily mean that the Hubble parameter is, at this moment, increasing.

I thought that the Hubble parameter was, in fact, still decreasing, so that the Hubble radius was increasing (the Hubble sphere was not shrinking down and getting closer as you say, but expanding and getting farther)

nevertheless I don't feel particularly strongly either way. If you want, show me a version of the Friedmann equation that says why the Hubble parameter is increasing---if that is what the official word on this is.

============
thanks in advance! just read your next post (#27) and since I can still edit I do not need an extra post to respond. I am satisfied. will let one of the others continue if they've questions about this.

 

[SpaceTiger]

I don't like to disagree, and this could be considered a minor point. I was under the impression that if one one limits one's view to the standard picture---Lambda CDM---then indeed expansion is accelerating. And all that means is that ä(t) is positive: the second time-derivative of the scale param is positive. AFAIK it does not necessarily mean that the Hubble parameter is increasing (so that the radius is diminishing and the sphere is getting closer)

So I was under the impression that this does NOT necessarily mean that the Hubble parameter is, at this moment, increasing.

That's absolutely correct, but remember that we're in comoving coordinates. A constant Hubble parameter (for example), leads to a Hubble radius that is constant in physical size, but shrinks in comoving size because the universe is expanding. It is the rate of change of the comoving Hubble radius that determines whether or not the light from distant galaxies ever becomes visible, not the rate of change of the physical Hubble radius.

 

[Jorrie]

Excellent, informative discussion guys - thanks very much!

 

[oldman]

The particle horizon is the experience-limiting boundary. The Hubble radius is not an actual horizon (just a scale distance) and the event horizon is the maximum comoving distance that can be causally influenced by us in the future.

Your identification of the particle horizon as the experience-limiting boundary --- what I have called the Horizon (with a capital H) --- is very definite, Space Tiger. Perhaps I can persuade you that the situation is not as simple as you or Marcus seem to imagine.

Consider the kinetics (not the dynamics) of a toy flat standard model universe, that somehow began suddenly. Suppose this universe does not expand at all, however unstable this situation may be. In this universe the Horizon is indeed the particle horizon, as you say. And, from the moment the universe "begins", the Horizon for all observers will recede from them at C.

Then consider a similar toy universe -- one that is eternal, and never did "begin". Let this universe expand perpetually, at a constant rate. Any observer in this universe will also have a Horizon, beyond which objects recede too fast for their light ever to reach him. In this universe there is no particle horizon. But there is an "event horizon" which provides his Horizon.

The model universe that cosmologists analyse is not like either of these toys. It has features of both, which complicates the classification of horizons. It "began", and it expands.

Now it becomes important to realize that any observer must regard the closest horizon to him as his Horizon. One, the particle horizon, moves away from him at c. The other is fixed eternally by the constant rate of expansion that determines the Hubble radius.

Then, just to make the analysis really tricky, in the cosmologists model the rate of expansion varies. Not just slowly, decelerating and then accelerating, as over the 13.7 billion years of expansion; but also dramatically, as during the instant of inflation. I have attempted to figure what the resulting behaviour of competing horizons is in my post #12. I now realize that it would have been prudent to float the above toy models first.

As to the second kind of difficulty that I have given the impression troubles me, which touches on your comment:

How can we know what will and won't be someday verifiable. I think it's best to leave the theoretical possibilities open and not try to force our own limitations on the universe itself

I agree with your sentiments.

To be more explicit; Marcus, you said:

I would guess from your post that you believe that if a galaxy is NOW receding faster than c, then no matter how long we wait we will never receive the light that it is emitting in our direction NOW.

If you believe this, please affirm. I happen to disagree and will try to persuade you to my viewpoint.

No, I don't believe this at all. But if you want to begin at the beginning with the horizon situation, I believe that it is useful to simplify by first ignoring dynamics (i.e. the Friedmann equation) and concentrate instead on the kinematics of horizons, about which the Friedmann Equation has nothing to say. I've tried this above. And thanks for letting me have the URL of that calculator, which I hope to make use of.

Second, about what we happen to our Horizon in the far future. I agree that it will change. But again to simplify, I prefer sorting out what has happened in the past before trying to figure this out. You see, Marcus, I suspect that my time horizon is somewhat shorter than yours --- I am, after all ---Oldman (aka The Mule). With best wishes.

Finally, a word to Jorrie, who kindly said:

Excellent, informative discussion guys

I reply: vasbyt!

 

[SpaceTiger]

Then consider a similar toy universe -- one that is eternal, and never did "begin". Let this universe expand perpetually, at a constant rate. Any observer in this universe will also have a Horizon, beyond which objects recede too fast for their light ever to reach him. In this universe there is no particle horizon. But there is an "event horizon" which provides his Horizon.

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).

The model universe that cosmologists analyse is not like either of these toys. It has features of both, which complicates the classification of horizons. It "began", and it expands.

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.

So, in the end, the situation is made simple again. Just treat the end of inflation as the "beginning" when calculating the particle horizon. The other complications (dark energy, radiation, dark matter, etc.) are all already incorporated into the calculation.

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.

 

[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.