Evolution of the Observable Universe

1. May 14, 2006

Chronos

Note from SpaceTiger: This discussion originated in the "what existed before the big bang?" thread.

Well put marcus. I think we are on the same page [albeit you are more eloquent] - and I tend toward being brutally blunt. We reside in an OBSERVABLE universe. And, by definition, it includes all things that are observationally accessible to us. The only apparent limit on this 'observable' universe, is time. It is, IMO, an exercise in futility [aka, unscientific] to fret about what [if any] unobservable regions might exist. I also reject the notion hitherto unobservable regions of the universe will eventually 'cross the line' and join the ranks of the observable. Wasn't that the whole point of introducing inflation?

Last edited by a moderator: May 16, 2006
2. May 14, 2006

marcus

probably this is a minor point but according to the mainstream cosmo model the observable universe is at present constantly growing, that is to say hitherto unobservable regions are constantly "crossing the line" and joining the ranks of the observable.

it is hard for me to imagine how this could be otherwise, at present, given the usual Lambda-CDM model that most of them regularly use. It is just a fact of geometry. But if I remember correctly this will not always be so!
Because of accelerating expansion (Lambda, say, in the usual model) one can estimate the ultimate radius of the observable.

I don't remember the numbers but it is something like this-----the PRESENT particle horizon or distance to the edge of the observable is, say, something like 47 billion LY and the ULTIMATE MAX that it will ever be is something like 60 billion LY. I dont remember the current estimate, roughly 60.
this is sometimes called the "cosmological (event) horizon"

we can not now receive signals from stuff that is currently 60 billion LY away. They arrived yet. But they are on their way if we WAIT LONG ENOUGH the signals will arrive.

If you dont care about the difference between 47 and 60 (or whatever the numbers are) then what you said is, in spirit, QUALITATIVELY CORRECT. there is not much difference-----acccording to the standard model.

but if you want to be finicky about it then what you said does disagree with the standard picture according to which the observable is expanding for now and will peak out at something like 60----so there are new regions crossing over the line all the time.

A discussion of this is in Lineweaver "Inflation and the CMB"-----he gives the numbers, says 62
http://arxiv.org/abs/astro-ph/0305179
===quote from page 14 of Lineweaver===
In Fig. 4 we see that the observable universe ( = particle horizon) in the new standard Lambda-CDM model approaches 62 billion light years in radius but will never extend further. That is as large as it gets. That is as far as we will ever be able to see. Too bad.
===endquote===

Last edited: May 14, 2006
3. May 15, 2006

Chronos

Interesting. It appears you are asserting spacetime expands faster than the matter embedded within it, rather than carrying it along with the Hubble flow.
Agreed, it is irrelevant. I'm only interested in the currently obsevable universe.
It's a matter of perspective. The CMB is our observational limit ~ 13.7 GLY. I do not foresee that changing any time soon. It is fun, but not very useful to speculate how 'big' the universe might 'really' be at this very moment.

Last edited: May 15, 2006
4. May 15, 2006

Garth

Not actually the case. It suggests the universe is decelerating in its expansion, which then creates a horizon problem at earlier epochs. As the current view is DE is acclerating the expansion then that would suggest we see less proportionally of the universe as time proceeds.

There is the question of course in the standard model as to whether the universe is still accelerating or not and that depends on DE's equation of state.

Garth

Last edited: May 15, 2006
5. May 15, 2006

marcus

In the Lineweaver article it is Lambda-CDM
which I guess you could call the STANDARD standard model
and with Lambda, equation of state w = -1 exactly

for me, it is too confusing if we start talking about a whole lot of different models without first agreeing on what the standard Lambda-CDM model says.

In that model, IIRC, the expansion is accelerating in the usual sense that a''(t) is positive (at present and for foreseeable)

and at the same time the hubble parameter H(t) is DECREASING (now and for the foreseeable) but it is decreasing more slowly and has an asymptotic value.

You recall that H = a'/a
so these two statements are not inconsistent.

And, IIRC, because H is decreasing, our observable region can be EXPANDING

and Lineweaver gives the present size of the observable as 47 GLY and the target as 62 GLY.

====================
Chronos,
there is going to be some variation in the numbers depending on details of what you plug in, but the 47 GLY is roughly right

if you are going to make sense of the universe at all then you need at least a figure for the density, which you estimate, in part, by counting galaxies in some volume.

if your idea of distance is wrong by a factor of 3 or more------like a person saying the distance to the edge of the observable is 13.7 instead of 47---then your galaxy-count density will be off by a factor of 9 or more. So you will screw up royally.

the reason for having a standard model like Lambda-CDM is to make numerical sense out of things

Don't knock it. It may not be right but it is a good start. and it is consistent.
the present distance of objects which we now see is a real thing, without a lot of logical slack to play around with

if the universe is expanding then that distance HAS to be larger than the light travel time multiplied by c. because of stretching.

if you believe the universe has expanded, then if the travel time is X billion years, the distance HAS to be bigger than X billion lightyears.

at least to me, it does not sound sensible to talk as if it were only X billion LY.

so it is really jarring to hear someone say that if the light travel-time from something is 13.7 GY then the distance to that thing must be 13.7 GLY.

It is as if that person is trying to claim the universe doesnt expand.

And what other meaning do you attribute to the word "distance" besides the actual present distance?

the distance which was the present distance at some moment in the past? OK which moment?

Last edited: May 15, 2006
6. May 16, 2006

Chronos

Temporal distance makes the accounting easier, marcus. Virtual distance is merely a puzzle box. The observable universe closes the curtain at about z = 1100. We cannot peer beyond that wall. Since we can still see the CMB [albeit crudely] we already see all that is observationally possible to see. The CMB will continue to receed, but will not add new objects as it marches towards redshift oblivion. What we could see [eventually] is hugely redshifted structures smear into view.

7. May 16, 2006

hellfire

The observable universe (the radial distance to the particle horizon) increases always. This is currently about 47 Gly. For a cosmological constant dominated universe a decreasing H means an increasing radial distance to the event horizon. With t $\rightarrow \infty$, DE.H. $\rightarrow$ c/H.

Last edited: May 16, 2006
8. May 16, 2006

marcus

I believe what you say is quite true and corresponds to what I was saying, the last time i worked this out was a couple of years ago and I got that H decreases to an assymptotic value----approaches a limit. and that was why the cosmological horizon has an upperbound (which it approaches as a limit) of around 62 GLY.

Even though I think your statement is mathematically correct, I cant tell if you agree with this or not. I am curious. Do you agree that the LambdaCDM model has a bounded event horizon----with some distance like 62 GLY?

I remember working it out, but this 62 figure I just pulled out of a standard reference work.

9. May 16, 2006

marcus

neutrinos
the cosmic neutrino background is not now being observed but with improved instruments it CAN be observed and that is what observABLE is about

the difference is between looking at photons from year 350,000 and looking at particles from when expansion is ~ 1 second old.

you are welcome to think in terms of "time-distance" if it suits you,
but from my perspective in an expanding universe the term is an oxymoron.
it does not correspond to the FRW metric that cosmologists actually use for measuring densities, calculating curvature--and generally modeling the dynamics of the universe.

It is fine to differ as long as we can be explicit about what distance measure each person is using.

10. May 16, 2006

hellfire

From the first Friedmann equation you can obtain the equation:

$$H = \frac{1}{a} H^0 \left( \Omega^0_m \frac{1}{a} + \Omega^0_r \frac{1}{a^2} + \Omega^0_k + \Omega^0_{\Lambda} a^2 \right)^ {1/2}$$

where the superscript 0 means at the current epoch. For a flat universe with $\Omega^0_k = 0$, when $a \rightarrow \infty$ you get:

$$H^{\infty} = H^0 \sqrt{\Omega^0_{\Lambda}}$$

Asymptotically the expansion will be de-Sitter and therefore the radial distance to the event horizon will be $D = c/H^{\infty} = c/H^0 \sqrt{\Omega^0_{\Lambda}} = D_H / \sqrt{\Omega^0_{\Lambda}}$ with DH the current Hubble length that is equal to 13.7 Gly.

With $\Omega^0_{\Lambda}$ = 0.73 you get D = 16 Gly. This value seams to agree with the upper diagram in figure 1 of Lineweaver's paper.

Last edited: May 16, 2006
11. May 16, 2006

marcus

good reference!
I would recommend anyone interested in such matters to glance at figure one. Especially the second and third panels. The bottom panel is the one I find easiest to read.

You can see there the maximum radius of the observable universe is 62 billion lightyears----read it right off the graph!

the paper hellfire referenced is
http://arxiv.org/abs/astro-ph/0310808
Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe
Tamara M. Davis, Charles H. Lineweaver

I find the top panel in figure 1 harder to read because I have to mentally convert the "proper distance" to co-moving and replot the graph in my head---so I am grateful that he includes the second and third panels that do the replotting for me!

the bottom panel because it is the biggest, and in convenient units, is very easy to read from and you can even see the radius of the observable is 46 billion lightyears.

this is the 47 I was talking about (trivial difference from plugging in slightly different parameters in the model)

so this figure 1 panel SHOWS GRAPHICALLY how the present horizon of 46 billion (that we are observing now) will evolve with time to the maximum of 62 billion lightyears, as more and more light comes in from farther and farther out.

thanks for the Lineweaver link, hellfire

Last edited: May 16, 2006
12. May 16, 2006

hellfire

But marcus, you are talking about the particle horizon. This does not have a maximal value as t $\rightarrow \infty$ but increases always with time as long as the universe does not contract. This is because light does always travel farther away. The figure 1 shows about 62 Gly because the diagrams are truncated. If you take a look to the time values at the left you see that only 25 Gy are depicted. If you imagine the first panel for time going to infinite you may visualize difference to the event horizon, that approaches asymptotically the value of about 16 Gly.

Last edited: May 16, 2006
13. May 16, 2006

marcus

This arguing back and forth could be a waste of time. I have no interest in convincing you of anything and am happy for you to believe whatever you want. I will state my position.

In present 2006 distance terms, our present lightcone extends out 47 GLY

Similarly, by the "end of time", that is as f-> oo, our lightcone will extend 62 GLY (present distance.)

this can be seen from the Lineweaver figure 1 that you cited.

but he also explicitly SAYS THIS in a better more detailed paper called 'Inflation and the Cosmic Microwave Background' which has the same figure, plus more explanation, and a bunch of other figures. You can look it up. He says the biggest piece of the universe we will EVER SEE (always assuming the standard LamdaCDM with usual parameters) is currently radius 62 Gly.

so there is crud that is currently 40-some Gly away from here which sent us some light a long time ago which is ONLY JUST NOW GETTING HERE

and there is crud which is currently 60-some Gly away which sent us some light a long time ago which WE HAVENT SEEN YET, BUT WE EVENTUALLY WILL

and there is some crud which is 70 Gly away which sent some light ages ago IN OUR DIRECTION BUT WHICH WILL NEVER GET HERE in the whole lifetime of the universe even if it lasts forever.

If anybody wants a reason to be humble, there is a huge amount of the universe, all the stuff currently more than 62 Gly away, which we will never see no matter how curious we are about it, even if we live to be infinity years old like your grandmother.

And moreover I am personally quite happy if you hellfire or anybody else WANTS TO DISBELIEVE THIS. Why not? It doesnt do any harm.

And moreover I could be wrong. Maybe I misread what Lineweaver was trying to say or something.

I have said my position. I will check "Inflation and the CMB" to make sure he has this, but otherwise dont need to discuss it further.

the other question about "what existed before bang" is still interesting

Yeah, I went and found the Lineweaver quote about the 62 billion lightyears. hadnt looked at that paper for a while, maybe a couple of years. great paper. some details need correcting but I dont think this does.
===========astro-ph/0305179========
page 14:
Five years ago most of us thought that as we waited patiently we would be rewarded with a view of more and more of the Universe and eventually, we hoped to see the full extent of the inflationary bubble – the size of the patch that inflated to form our Universe. However, Lambda has interrupted these dreams of unfettered empiricism. We now think there is an upper limit to the comoving size of the observable universe. In Fig. 4 we see that the observable universe ( = particle horizon) in the new standard LambdaCDM model approaches 62 billion light years in radius but will never extend further. That is as large as it gets. That is as far as we will ever be able to see. Too bad.
===============endquote==========

Last edited: May 16, 2006
14. May 16, 2006

hellfire

marcus, I don't think this is a question of belief, but basically of definitions. Of course I may be wrong, but then I would appreciate it if you point out my mistakes because this is the only way to learn.

It may be useful to consider the example of a de-Sitter expansion. The scale factor is:

$$a = e^{Ht}$$

With H a constant Hubble parameter.

If you take the definition in comoving coordinates of the particle horizon for $t = \infty[/tex] as stated in equation (7) in Lineweaver's Inflation and the Cosmic Microwave Background you get: $$\chi_{ph} = \int^t_0 dt/a = \int^{\infty}_0 dt e^{-Ht} = \frac{1}{H}$$ This would mean that in an exponentially expanding space the particle horizon is at a constant comoving distance of the observer. Since our universe tends asymptotically to an exponential expansion, the particle horizon will have a maximum comoving radius at t [itex]\rightarrow \infty$. So you are right if you are talking about comoving distances.

However, distances can be defined also as proper distances on a surface of constant time. In my opinion this is the most natural definition of distance, as it enters the Hubble law and it is the distance that you would measure having a rod, same as the distances you measure every day:

$$D = a \chi$$

See equation (2) of Lineweaver's paper. With this definition:

$$D_{ph} = a \frac{1}{H} = e^{Ht}\frac{1}{H}$$

Which is increasing with time. For the event horizon something similar applies.

I would say that the number of objects we can observe depends on the distance on a surface of constant time from which light reaches us. In an hypothetical universe with constant density of objects in space as well as in time an increasing proper distance of the particle horizon implies more and more objects to be visible. Thus the "observable universe" increases always. I am aware that this claim of mine is in contradiction with Lineaweaver's claim you have quoted. This puzzles me, however, I am not able to see the mistakes in my arguments, if any.

Last edited: May 16, 2006
15. May 16, 2006

marcus

Hi hellfire, I think we can harmonize ideas. I will suggest something you can try out with your equations and in your own mind to see if it works. You must be the judge.

What I am saying is that the farthest crud that we will EVER see is crud that at the present time is 62 Gly from us.

so that defines a kind of ultimately observable spherical chunk of the universe. what i am talking about is the OBJECTS, the matter etc that is in that sphere.

I am using the distance only to define a set of objects which is ultimately observable and outside of that the objects will never be.

But BY THE TIME WE ARE OBSERVING THOSE OBJECTS they will be way mondo further away than 62 Gly in the FRW metric distance measure that we are using THEN.

Personally the distance estimated by a person living 100 billion years in the future does not interest me so much, I am more interested in knowing the OBJECTS WHICH ARE AVAILABLE FOR STUDY.
But if you wait long enough those objects that are now 62 Gly from us will be as far as you please. they will be arbitrarily far away.

So we can both be right, if you care about this. I will say that there is an absolute eternal limit to the observable and in comoving distance----the real present distance by the FRW metric at this moment----this limit is exactly 62 Gly out.
and you can say that the observable will be arbitrarily far out if you wait indefinitely long. the radius of the observable in future metrics GOES TO INFINITY.

Speaking in the limit, as t -> oo, after a while observable does not include any new objects, but those objects in observable get farther away.

Perhaps this is what you meant all along and I didnt realize we were saying the same thing???

16. May 17, 2006

Chronos

I think we have all been saying pretty much the same thing all along, just disagreeing on how to phrase it. I'm not interested in the current, actual size of the universe, just the observable time slice.

Footnote: Agreed, marcus, with a neutrino telescope we could pierce the surface of last scattering fog and peer into an even more temporally remote time slice.

Last edited: May 17, 2006
17. May 17, 2006

hellfire

Yes, you and Lineweaver are right. I was wrong when I claimed in my last post that always new objects will be visible. I will explain the technical reason for this. First, let's summarize the result from the calculations above: In a de-Sitter model, that can be regarded as the asymptotic limit of our universe, the particle horizon (the current location of the most distant objects or crud whose light we are receiving today) reaches a constant comoving distance when t $\rightarrow \infty$, but increases always its proper distance. So far we have not said anything about new crud that is located farther away.

Speaking about comoving or proper distances is a matter of definitions and conventions. The question to understand Lineweaver's claim is the following: If a particle horizon is at constant comoving distance of a comoving observer, does the crud that is located farther away decrease its comoving distance and enter the particle horizon? Equivalently, if the proper distance to the particle horizon increases at a given rate, does the crud that is farther away increase its proper distance to us slower so that it can enter the particle horizon?

The easy question to approach is the first one. The point is that, due to the definition of comoving distance, comoving objects and crud located at a comoving distance Dc will be always located at the comoving distance Dc during the expansion of space. They will be located at a larger proper distance in new spatial hypersurfaces, but their comoving distance will be the same. This means that no new crud can enter the particle horizon if the particle horizon it is located at constant comoving distance of us.

18. May 17, 2006

marcus

I didnt follow everything but I think you are probably right. I think it is a very interesting topic and wish more people would discuss what is the ultimate horizon of the ultimately observable universe. And I would say you hellfire are in charge of the thread from this point (I dont think I have any more thoughts about it).

Last edited: May 17, 2006
19. May 18, 2006

hellfire

Who is not confused? Horizons are weird.

For black holes, matter can only cross the horizon from the outside to the inside. Without considering quantum effects, the horizon area can only increase or stay constant according to the generalized second law of thermodynamics for asymptotic observers outside. Considering a quantum scalar field, as usual, the horizon area may decrease due to the thermal Hawking radiation that transports entropy out of the black hole.

In case of a de-Sitter horizon, matter can only cross the horizon from the inside to the outside. If we assume that something similar to the generalized second law applies for comoving observers inside, and without considering quantum effects, the horizon area on a hypersurface of constant time can only increase or stay constant.

However, considering a quantum scalar field, the de-Sitter horizon does also radiate towards the comoving observer inside. Does this mean that it may also decrease its area?

What does this entropy measure?

20. May 19, 2006

Chronos

A fairly confusing discussion. How/why did 'horizons' creep into this conversation?