Universe expanding faster than light

[camilus]

I read it is possible for the universe to be expanding faster than the speed of light.

What would be the implications of this?

 

[DaveC426913]

I read it is possible for the universe to be expanding faster than the speed of light.

What would be the implications of this?

The speed limit of the universe applies locally. The expansion of the universe is the expansion of the space - no object is moving faster than c locally, so it does not violate SR.

However, the expansion will prevent us from seeing anything that's moving away faster than c.

Search this forum for "superluminal expansion".

 

[sylas]

However, the expansion will prevent us from seeing anything that's moving away faster than c.

Most of the galaxies we see in deep space are "moving" (or receding) faster than the speed of light. They have always been receding faster than the speed of light.

Search this forum for "superluminal expansion".

You need to be careful. There are sometimes people who confidently make statements that are not true. Sorry Dave, you just did this here yourself.

That's part of the fun... many people here are amateurs trying their hand at learning and explaining what they've learned; but we sometimes make mistakes. There are also a number of professionals here who know and understand the details very well. It can take time to sort out who is who. I'm not one of the experts; but I know a bit about it... and I've been picked up by the experts from time to time as well!

I'll see if I can find a good thread on this. There are some confusing threads as well.

Cheers -- sylas

 

[camilus]

The speed limit of the universe applies locally. The expansion of the universe is the expansion of the space - no object is moving faster than c locally, so it does not violate SR.

I perfectly understand this, I know that expanding faster than c doesn't violate the 'cosmic speed limit' because it is space itself that's expanding, not a particle in space moving faster than c.

However, the expansion will prevent us from seeing anything that's moving away faster than c.

Search this forum for "superluminal expansion".

Thats my initial thought as well. But if the rate of this expansion is in fact superluminal, what can we say about the size of the universe? Cant it be a lot bigger than we think. since we can't see that far?

Im going to do the search now, thanks.

 

[sylas]

Im going to do the search now, thanks.

Perhaps more useful would be a tutorial reference. See, for example, the well regarded cosmology tutorial by Ned Wright. Also his FAQ on this very question:

Can objects move away from us faster than the speed of light?

Again, this is a question that depends on which of the many distance definitions one uses. However, if we assume that the distance of an object at time t is the distance from our position at time t to the object's position at time t measured by a set of observers moving with the expansion of the Universe, and all making their observations when they see the Universe as having age t, then the velocity (change in D per change in t) can definitely be larger than the speed of light. This is not a contradiction of special relativity because this distance is not the same as the spatial distance used in SR, and the age of the Universe is not the same as the time used in SR. [...]​

 

[marcus]

...

However, the expansion will prevent us from seeing anything that's moving away faster than c.
...

That is not quite true. For example there are thousands of galaxies with redshift around z = 1.5.

A galaxy which we see with redshift 1.5 is today moving away from us faster than c.

However according to standard cosmo, someone in such a galaxy could send us a message today, and it would get here.

The reason this works is because the Hubble rate is decreasing and will be decreasing for the foreseeable future. This means that the Hubble distance (c/H, reciprocal to the rate) is increasing.

This is explained in Lineweaver's SciAm article "Misconceptions about the Big Bang". I have a link to it in my sig.

 

[DaveC426913]

Most of the galaxies we see in deep space are "moving" (or receding) faster than the speed of light. They have always been receding faster than the speed of light.



You need to be careful. There are sometimes people who confidently make statements that are not true. Sorry Dave, you just did this here yourself.

That one always throws me. I defer to greater wisdom.

 

[marcus]

Sylas, I think the word is "kudos" or maybe it is "thanks". Not for your contribution to this thread in particular, but on several astro/cosmo threads I've been seeing clear reliable helpful posts of yours. It seems to help.
Thanks and kudos.

I also would warn against searching PF for "superluminal expansion". The fact that someone uses that term even suggests they may not understand normal cosmo very well. It is typical for largescale distances to expand at rates > c.

I think your idea of Ned Wright's tutorial is a good suggestion.

Most of the galaxies we can see are at distances which were expanding > c when they emitted the light and which continue now to expand > c. That is true for anything with redshift 1.7 or greater. And of course we are getting the light from them--it reaches us nevertheless.

And of course these galaxies are not moving significantly, they are not going anywhere in particular. Individual motions are generally only a few 100 km/s which is negligible compared with c.

 

[marcus]

Thats my initial thought as well. But if the rate of this expansion is in fact superluminal, what can we say about the size of the universe? Cant it be a lot bigger than we think. since we can't see that far?

Well it's intelligent to ask if there are consequences of expansion. But basically expansion is just Hubble law, which says that on large scaler the actual (the present day or "now") distance is increasing 1/140 of a percent per million years. That doesn't apply to local in-galaxy distances, among gravitationally bound objects.

Superluminality is a non-issue because of course if you take a large enough distance, like an actual distance of 14 billion LY, that distance will be increasing c or more, just work out the percentage! At 1/140 percent, it will grow by a million LY in the course of a million years. I'm talking actual distance. That rate of increase---a million LY in a million years---is c.

And astronomers have been living with Hubble law (which is what I'm talking about) since 1929.

So they have had time to get used to expansion, and their ideas of the size of the universe and the distances to various horizons are comfortably compatible with the expansion model and the Hubble law.

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

You asked about current size estimates. This is a separate issue. If space is infinite then it is infinite, right? So what if it is finite. When astronomers discuss that case they typically are talking about a 3D hypersphere and the question comes down to estimating a lower bound on the circumference.

Currently, according to the most recent authoritative report, Komatsu et al, March 2008 from NASA's WMAP mission, there is a 95 percent confidence estimate for the circumference of 600 billion LY.
I'll get the link for you later, unless someone else does. I have to go to supper now.
Back now. To get that report you just google "komatsu wmap" and it will be the fourth hit or so or you google
"komatsu wmap cosmology" and it will be the first hit. The reports were published in 2009 although the preprints came out in 2008.
The key thing is you want "Cosmological Interpretations" report. Table 2 on like page 3. You have to know the units they are using, but if you work it out it comes to a circumference of some 600-630 billion LY, lower bound with 95% confidence.

That is actual distance ("now distance") meaning you freeze expansion and send off a flash of light and it will take 600 billion years before it comes around and you see it coming in from opposite side of the sky.

There are other types of distance and coordinates, which are interesting to discuss once you learn the basics, and of course distance depends on coordinates. But this now distance or actual presentday distance is what the professionals most commonly use, and it's what works in Hubble Law. So it is the good one to get started with.

 

[Phrak]

I read it is possible for the universe to be expanding faster than the speed of light.

What would be the implications of this?

If the answer is yes, what does it mean?

It means you take a local map of spacetime that is nice and flat (said to have a Minkowski metric) and apply it to the spacetime of distant regions.

Are the values of velocities for distant objects and radiation intrinsic properties, or are they an artifact of the map?

 

[marcus]

Are the values of velocities for distant objects and radiation intrinsic properties, or are they an artifact of the map?

Once you choose a map, then everything you derive from using that map must derive ipso facto from that map.

That's not the point. The question is what kind of coordinates and what kind of basic distance measure do cosmologists actually use. We have an educational responsibility to use terms and concepts compatible with normal cosmology. They use the Friedman metric and the Friedman equations are the basic model.

They don't use the Minkowski metric---trying to force the universe to fit on a Minkowski rack would be horribly impractical. Minkowski spacetime has no expansion. You can think of the universe as spatially flat or nearly flat, so you might think Minkowski would be a good fit. But don't confuse spatial flatness with overall spacetime being Minkowski.

By contrast the 1922 Friedman metric, which is what cosmologists are still using, and mostly very happy with, has built in expansion and is considerably more comfortable to use. Friedman metric is the language the Hubble Law talks and the Friedman equations which are about that metric, are the basic equations of cosmology.

Friedman let's you say easily what it means to be at rest with respect to the ancient matter of the universe, or the afterglow from it, the cosmic microwave background. And it turns out that galaxies have very small individual motion with respect to background, most matter is approximately rest.

If you pick some peculiar coordinates then to get a fit you will have to strain and force things---like it may force galaxies to be whizzing away from some arbitrarily chosen centerpoint at stupendous speeds. Actual motion (in terms of your different choice of coordinates.)

 

[Chronos]

Other interpretations are possible, marcus. I perceive no need to portray any particular model as the only one worth considering.

 

[Phrak]

Once you choose a map, then everything you derive from using that map must derive ipso facto from that map.

That's not the point. The question is what kind of coordinates and what kind of basic distance measure do cosmologists actually use. We have an educational responsibility to use terms and concepts compatible with normal cosmology. They use the Friedman metric and the Friedman equations are the basic model.

I read it is possible for the universe to be expanding faster than the speed of light.

What would be the implications of this?

I didn't read between the lines. What did I not see.

 

[Chalnoth]

Most of the galaxies we see in deep space are "moving" (or receding) faster than the speed of light. They have always been receding faster than the speed of light.

I don't think this is actually true. First, I'd like to make a pedantic point:

In General Relativity, the operation of subtracting one velocity from another to get relative motion is only well-defined at a single point. So if I want to talk about recession velocity, it turns out that the question is very ambiguous, and whether or not such velocities exceed the speed of light just depend upon what ambiguous definition we choose. For example, if a far-off object is at rest with respect to the universe, and we are at rest with respect to the universe (we aren't, quite, but this is just a thought experiment), then we could just as easily state that we are neither moving towards or away from this far-off object as we could state that this object is receding at faster than the speed of light. This ambiguity is unavoidable due to the nature of General Relativity, and is precisely why "faster than light recession" is not a problem: if the way in which you compare velocities of objects far away from one another is ambiguous, then there certainly can be no law limiting such velocities.

The actual speed of light limitation in GR is that no object can outrun a light beam. That is, no matter where the object is, and no matter what your perspective of looking at that object is, that object will always be moving more slowly than the photons in that object's vicinity.

Now, with that out of the way, we can define a very simple recession velocity:

v = Hd.

This is sort of what we naturally think of when we think recession, and I'll use this definition from here on out. With this definition, the distance at which things start to exceed the speed of light is about 14 billion light years away. As marcus points out, in terms of redshift this is about z = 1.5 or so. We currently can see galaxies out beyond redshift 7, and the CMB is at a whopping redshift of 1090.

The solution to this apparent problem is just that we have to take into account how the universe has expanded from the time the light was emitted to now. To take a look at the distance today of these objects, and notice that the Hubble law predicts a recession velocity greater than c, and then scratch our heads wondering why we can see these objects, is missing the point.

First, we can't say, without looking in more detail, whether or not these objects were receding faster than light. They might have been: as long as the universe reduced its expansion enough in the interim, we might see them today.

But what if the object today is expanding faster than light, and always will be? Well, in that case, we can never observe it. The distance at which this occurs depends upon the future expansion of the universe, which we don't yet know for certain, but if the correct explanation for dark energy is a cosmological constant, or something that has the future behavior of the cosmological constant, then stuff that is currently receding at faster than the speed of light (beyond about 14 billion light years, or redshift 1.5) is currently emitting photons that we will never ever see, no matter how long we wait.

Yes, this means that many objects visible today have already passed out of causal contact. This does not mean that they will disappear. But what it does mean is that we will never see them age past 13.7 billion years old (the current age of the universe): all of the photons they emit after that time will never reach us.

If, on the other hand, the expansion were to slow again, then we may start to see some of the photons from later in these objects' lives. For instance, for much of the early history of our universe, the expansion was slowing down. So the norm would have been to see far-off objects that were, when the light was emitted, receding faster than light, but currently are not. Today the converse is true due to the recent accelerated expansion.

All that said, it is just patently incorrect to state that we can see objects today there have always been receding at faster than the speed of light.

 

[marcus]

Most of the galaxies we see in deep space are "moving" (or receding) faster than the speed of light.
...

I don't think this is actually true.

... it is just patently incorrect to state that we can see objects today there have always been receding at faster than the speed of light.

Chalnoth, I don't understand your reasoning, or why you say that. Let me explain.
There are objects that we see today which have always been receding faster than c, and indeed this is typical.
Have a look at Lineweaver, the link is in my sig, to understand how that happens intuitively. He has a graphic illustration. What you seem to be saying is one of the common misconceptions about expansion cosmo, i.e. that it is impossible for us to be be seeing light from objects which have always been receding faster than c.

We can do the numbers if you would google "cosmos calculator" and put in .25, .75, 74 (the current best parameters) and try some redshift like 1.7.
If you put in z = 1.7 you will get that the recession rate then (when light emitted) was 1.01c and the recession rate now (when light received) is 1.14c.
So that thing was receeding all that time > c. But the light got here.

Now you can put in z = 1.8 , or 2.0, or 2.5, and so on and you will find the same story except all the recession rates are higher. In other words what Sylas said is even more true the farther past z = 1.7 you go.

But there are way more objects with z > 1.7 than with z < 1.7. So one can easily conclude that it is typical, that when we see some galaxy probably that galaxy was receding > c when it emitted the light, and also all the time since then.

Physically it is easy to understand how the light gets here despite losing ground at first. The Hubble rate H(t) decreases and that makes the Hubble distance increase and the Hubble distance so to speak reaches out to the struggling photon. Once the photon is within the Hubble distance then it can make forwards progress and get closer to us and gradually make it here. That is kind of figurative, not a rigorous description, but you can make it rigorous.

Then also notice that even though we have acceleration and a''(t) > 0, the Hubble rate has always been decreasing and is destined to continue to decrease according to the standard cosmo model.

I guess the asymptotic value for H(t) will be about sqrt(.75) times 74. Let us see what that is. It comes out to 64. So H(t) will decline from present 74 and approach 64 from above. This is just what the standard model predicts. Of course we do not know the future.
But going by the standard model, we see that the Hubble distance still has another 15 percent to expand. From the present 13.2 out to 15.3 billion LY.
That means that any photon which can manage to stay within 15.3 billion LY of us, and is heading our way, will eventually make it to us.

But what if the object today is expanding faster than light, and always will be? Well, in that case, we can never observe it.

I don;t think that is right. A galaxy which is today just outside the Hubble radius could send us a message today which would reach us. The Hubble radius is the current distance of objects which are receding at c. Using the most recent parameters the Hubble distance is about 13.2 billion LY or a redshift of 1.4 (more precisely maybe 1.38 but let's say 1.4). The Hubble distance is supposed to expand in the future out to 15.3 billion LY (that is the "cosmological event horizon").

Something out there at 15.3 billion LY can not send us a message. And we could not get to them even if we could leave today and travel at speed c.
So it's like you said about out of causal contact. But 13.2 is not the same as 15.3. There is some leeway, so to speak. Some slack. I estimate a galaxy which for example is now out at 14 billion LY could send us a message today that would get here even though it is receding at a rate > c. I will try to double check that. Havent done the numbers rigorously on it.
14 billion LY corresponds to a redshift z = 1.5 and a presentday recession rate of 1.06 c. So at first the photons would be "swept back" so to speak at the rate 0.06c. But they have 1.3 billion LY of leeway before they hit the limit of 15.3 billion LY. Even if they lost ground at an average rate of 0.1c for 10 billion years that is still only a loss of 1 billion LY and they would then be 15 billion LY from us. Before those 10 billion years have passed I think the Hubble distance will have extended out to them and they will be making progress towards us. I'm sure you see how it works. I'll have to figure out how to do the example more rigorously though.

 

[yogi]

Other interpretations are possible, marcus. I perceive no need to portray any particular model as the only one worth considering.

I would agree - and while having learned much from reading marcus's informative and well written tutorials, the standard model of mainstream cosmology should be qualified. History has shown that the majority is seldom right.

 

[marcus]

I would agree - and while having learned much from reading marcus's informative and well written tutorials, the standard model of mainstream cosmology should be qualified..

Thanks for your courtesy, yogi! I am a fan of some nonstandard cosmology and am excited by the progress it is making, but I think with newcomers asking basic questions we have a responsibility to give them the mainstream standard model first. They should get clear on that, as basics.

I personally perceive no need to portray any particular model as the only one worth considering.

And I do not myself portray any particular model as the only one worth considering.

My experience is that most newcomers arrive with some misconceptions about the mainstream model, gotten from some badly written popularization, or some oversimplification they heard, and they are puzzled by it. What they want first is to understand the mainstream picture and see why it makes sense. So that's our first job.

Once everybody is up to speed on mainstream basics it's great to explore how you can go beyond the standard cosmology model. For example with quantum cosmology---cosmology based on quantum general relativity---models that remove the singularity and go back earlier in time, for example.

 

[sylas]

I don't think this is actually true. ...

It is true. You can take it to the bank. Technically, it depends on what you mean by distance; but by pretty much any useful measure of distance we are seeing plenty of galaxies that are now and always have been receding faster than light speed.

There are certainly open questions about the nature of the universe and appropriate models and what lies beyond the observable horizon... but this is not one of those open questions.

[...] First, I'd like to make a pedantic point:

In General Relativity, the operation of subtracting one velocity from another to get relative motion is only well-defined at a single point. So if I want to talk about recession velocity, it turns out that the question is very ambiguous, and whether or not such velocities exceed the speed of light just depend upon what ambiguous definition we choose. [...]

You can indeed give different definitions, but that is not a case of "ambiguity" unless you fail to indicate what definition of distance you are using.

I like to use "proper distance", and recession velocity is simply the rate of change of proper distance with time. Proper distance seems to fit most closely with what we think of as distance conventionally. You can define it as the distance that would be measured if space was filled with co-moving rulers, that measure distance locally using their local clock and the distance moved locally by light in their immediate neighbourhood.

The "co-moving" distance is also very convenient in analysis; and by that measure, distant galaxies are mostly at a fixed distance, but with small local motions imposed. It's not really what you first think of as distance, however. With this co-ordinate, the "speed" of light or indeed any unaccelerated particle is continually reducing.

The actual speed of light limitation in GR is that no object can outrun a light beam. That is, no matter where the object is, and no matter what your perspective of looking at that object is, that object will always be moving more slowly than the photons in that object's vicinity.

YES. Exactly true.

Now, with that out of the way, we can define a very simple recession velocity:

v = Hd.

Yes. This is in fact what you get with "proper distance" d... except that you need to be clear when you are taking the definition. H varies with time. If you are using H as the expansion rate NOW, then v becomes the recession velocity now, and d is the proper distance now.

You could also define a recession velocity at the time we actually see the remote galaxy. In this case, you would use d at the time of emission (which will be much smaller) and H at the time of emission (which will be much larger) for a roughly similar recession velocity... and one which will still be much greater than 3*10⁸ m/s for most of the galaxies we can actually observe in deep space.

This is sort of what we naturally think of when we think recession, and I'll use this definition from here on out. With this definition, the distance at which things start to exceed the speed of light is about 14 billion light years away. As marcus points out, in terms of redshift this is about z = 1.5 or so. We currently can see galaxies out beyond redshift 7, and the CMB is at a whopping redshift of 1090.

Yes, to all the above. This is what we naturally think of with recession, and it uses what we generally think of with distances; and which is more precisely defined as "proper distance" in cosmology.

The solution to this apparent problem is just that we have to take into account how the universe has expanded from the time the light was emitted to now. To take a look at the distance today of these objects, and notice that the Hubble law predicts a recession velocity greater than c, and then scratch our heads wondering why we can see these objects, is missing the point.

No, it is exactly the point. It is often the case for a student of cosmology that it is breakthrough point of understanding when they grasp why we see those objects. It is something well worth understanding.

The proper distance "d" between us and an approaching photon emitted from deep space will initially be increasing. That is, even though the photon is moving locally towards us, the distance between us and the photon is getting greater.

Here's the key, however... as the photon passes through space, it comes to regions where the recession velocity is less and less. So the rate at which the distance between us and the photon increases is falling. It's not actually an acceleration, but the units are similar. Eventually, the sign reverses, when the photon is at a maximum proper separation distance. Thereafter, the proper distance between us an an approaching photon starts to reduce, until eventually the photon reaches us, moving locally at the speed of light ... as it has been doing all along.

First, we can't say, without looking in more detail, whether or not these objects were receding faster than light. They might have been: as long as the universe reduced its expansion enough in the interim, we might see them today.

No. That is just wrong. You can still see photons which are emitted from galaxies receding at greater than light speed, even if the rate of expansion is accelerating. The critical point is the simple exponential expansion in the simple pure inflation model. In that case, photons DON'T "catch up" with the expansion of space, and it would be impossible to see galaxies with recession velocity greater than c. But for a less drastic acceleration of the expansion rate... such as is proposed in the current consensus model with an effectively flat universe with some dark energy and sub-critical matter density... a photon can STILL get to us even if emitted from a galaxy receding at greater than light speed.

But what if the object today is expanding faster than light, and always will be? Well, in that case, we can never observe it. ...

No. That's just incorrect. There's no two ways on this; it's not a matter of opinion. There's no ambiguity about the world line of a photon in a given formal model for the universe, and there's no question that a photon can indeed cross the space between two galaxies which are receding from each other with the expansion of space with a recession velocity that is always greater than c.

There are questions in sorting out precisely what formal model corresponds to our actual real universe; but none of that has any bearing on the simple mathematical fact that when using your definition of recession velocity (which is the same as I have been using) and the FRW models for expansion of space, light can go from one galaxy to another even when they are receding at greater than light speed.

Cheers -- sylas

 

[Chalnoth]

Ah, right, sorry. I was failing to take into account an important fact: once the photon has left the object in question, it doesn't actually matter what that object does. It matters, instead, what the photon does. Even if the object retains a recession velocity greater than c, a photon which was emitted some time ago will be closer to us than the galaxy, and so won't have the same recession velocity to fight against, and so may well reach us.

However, far enough away, and it will always have more space to travel ahead of it than it crosses, and so it will never reach us.

 

[sylas]

Ah, right, sorry. I was failing to take into account an important fact: once the photon has left the object in question, it doesn't actually matter what that object does. It matters, instead, what the photon does. Even if the object retains a recession velocity greater than c, a photon which was emitted some time ago will be closer to us than the galaxy, and so won't have the same recession velocity to fight against, and so may well reach us.

That is a really clear and concise statement. I'm going to steal it for future use, with your permission!

However, far enough away, and it will always have more space to travel ahead of it than it crosses, and so it will never reach us.

It depends on how the expansion rate develops. In a matter dominated universe, or an empty (constant expansion) universe, then no; photons from arbitrarily far away will reach us.

But in the current consensus model, with dark energy and subcritical matter, I think you may be correct... but I am not sure. I have not tried to prove it one way or the other. Marcus might know...

Cheers -- sylas

 

[Chalnoth]

That is a really clear and concise statement. I'm going to steal it for future use, with your permission!

Certainly :)

It depends on how the expansion rate develops. In a matter dominated universe, or an empty (constant expansion) universe, then no; photons from arbitrarily far away will reach us.

Quite right. I addressed this point in my previous post, but was just a bit short for the sake of brevity here. What I said is accurate if the correct explanation for the accelerated expansion is dark energy or something similar. Otherwise...it depends.

But in the current consensus model, with dark energy and subcritical matter, I think you may be correct... but I am not sure. I have not tried to prove it one way or the other. Marcus might know...

Yes, actually, this one I'm certain about. I'm not used to thinking in terms of recession velocity, hence my previous mistake. But this is a standard result for de Sitter cosmology (which our universe will asymptotically approach if dark energy = cosmological constant): light can only travel a finite distance in comoving coordinates in de Sitter space.

To see this, consider the following. Take the FRW metric, neglecting the angular terms, and just taking the radial distance:

$$ds^2 = c^2 dt^2 - a(t)^2 dr^2$$

A light ray will move along a null geodesic, where $$ds^2 = 0$$, so we can get the path of light in the radial direction simply:
$$c dt = a(t) dr$$

If I want to know how far light has traveled in comoving coordinates, then, I integrate:
$$r = c \int_{t_1}^{t_2} \frac{dt}{a(t)}$$

So, for instance, if I want to ask how far, in comoving coordinates, a photon gets in infinite time, then I integrate:
$$r = c \int_{t_0}^{\infty} \frac{dt}{a(t)}$$

However, we typically don't work in these coordinates, so it is useful to change variables. The first change will be to use the definition of the Hubble parameter to change the integration from an integration in time to an integration over the scale factor:

$$H \equiv \frac{\dot{a}}{a}$$
$$dt = da \frac{dt}{da} = \frac{da}{a H}$$

This turns our integral into:

$$r = c \int_1^{\infty} \frac{da}{a^2 H}$$

Now, obviously this is only going to work for a universe that expands infinitely into the future (as only if the expansion continues indefinitely will $$a\rightarrow\infty$$ as $$t\rightarrow\infty$$), but if the universe starts to collapse obviously all points will come in causal contact regardless.

So, then, if you know your integrals, you should be aware that if the Hubble parameter H approaches a constant value, then the above integral approaches a finite value. Specifically, if H is constant, the integral is:

$$r = \frac{c}{H} \left[\frac{-1}{a}\right]_1^\infty = \frac{c}{H}$$

Which is the statement that in a de Sitter universe (one where we only have a cosmological constant), we reach the conclusion that an object with a recession velocity equal to the speed of light or greater today is emitting photons that we will never see, and we are emitting photons that will never reach them.

Of course, we're not in a perfectly de Sitter universe, so this isn't actually true: H is decreasing with time, which corresponds to a somewhat larger distance at which things will eventually communicate. Using $$\Omega_m = 0.27$$ and $$\Omega_\Lambda = 0.73$$, I get $$r = 1.12 \frac{c}{H_0}$$. So objects currently receding up to about 12% higher than the speed of light are emitting photons that we will detect at some point. But beyond that, we can never see those photons (and bear in mind that this is assuming the cosmology is accurate, which is by no means certain).

 

[sylas]

Of course, we're not in a perfectly de Sitter universe, so this isn't actually true: H is decreasing with time, which corresponds to a somewhat larger distance at which things will eventually communicate. Using $$\Omega_m = 0.27$$ and $$\Omega_\Lambda = 0.73$$, I get $$r = 1.12 \frac{c}{H_0}$$. So objects currently receding up to about 12% higher than the speed of light are emitting photons that we will detect at some point. But beyond that, we can never see those photons (and bear in mind that this is assuming the cosmology is accurate, which is by no means certain).

We are again all on the same page. I'm with you entirely on the de Sitter space; and given that the ratio of Ω_V to Ω_m approaches 1 (for a simple constant dark energy) the consensus model approaches de Sitter space. But I've not actually gone through the with calculation myself of 1.12 you give for the horizon of visibility in this model.

Thanks -- sylas

 

[Naty1]

Some implications (back to the original question):

I'll bet there are many implications that have not yet even been thought through nor even conceived! (let's hope so.)

We are likely able to currently observe only an infinitesimal portion of our own universe.

Nobody knew about an expanding universe until recently, via Hubble's observations. As noted already, consensus science is rarely right early on. Einstein was sure the universe was static.

Our own universe is really,really big. Beyond imagination.

Not only can we tell distant things are moving at greater than c, their movement away from us is now accelerating: the cosmological driving force, perhaps dark energy, is barely understood and it's recent discovery should serve as a humbling reminder: we just figured out that between dark energy and dark matter we don't know diddly about 96% of our own universe.

What we can see in our own universe may not explain anything about an infinite number of additional universes, nor if they even exist. Are we unique or one of many?

They fact that distant galaxies are expanding at a rate greater than "c" does not mean we can never observer them, only that we can't observe some right now.

Because it takes light from great distances so long to reach us, the most distant points observable appear as they were at earlier times. The "oldest light" (from the greatest distances) reaching us reflects cosmological structure even before galaxies were formed and all that existed was ionized gas...before that, photons could not escape the primordial plasma soup.

If all this keeps up, we'll be able to see more and more of an increasingly smaller proportion of our own universe.

 

[Chalnoth]

They fact that distant galaxies are expanding at a rate greater than "c" does not mean we can never observer them, only that we can't observe some right now.

Well, no, actually it doesn't mean this. Because the Hubble parameter has been decreasing with time, galaxies that have always been receding faster than c, and are currently doing so, are actually visible. There is a limit to how far we can see, but it's not so simple or obvious. Instead, the limit to our vision is the CMB (before which the universe was opaque), which denotes a surface that currently lies at roughly 45 billion light years away or so.

 

[marcus]

Using $$\Omega_m = 0.27$$ and $$\Omega_\Lambda = 0.73$$, I get $$r = 1.12 \frac{c}{H_0}$$. So objects currently receding up to about 12% higher than the speed of light are emitting photons that we will detect at some point. ...

We are again all on the same page... I've not actually gone through the with calculation myself of 1.12 you give for the horizon of visibility in this model.

Amen! Thanks Chalnoth! I trust your calculation and am glad not to have to do it. As an incidental BTW comment, Ned Wright has headlined the new HST-based estimate of the Hubble rate, 74 rather than 71 (with tighter error bounds). For a long time we've used (.27, .73, 71) as the chief parameters of the standard LCDM model. Now I think the new recommended parameters are (.25, .75, 74). It doesn't make much difference. But I have begun trying to get used to the new ones.

The new parameters lead to the conclusion that the Hubble distance is currently 13.2 billion LY and will eventually expand out to 15.3---coinciding (in the limit) with the cosmological event horizon.

All this discussion assumes we are talking proper distance. Here's where I calculated that 15.3. It's trivial. In the LCDM the energy density eventually goes to 0.75 of what it is today and putting that into the Friedman equations tells what the Hubble rate will be in the limit.

I guess the asymptotic value for H(t) will be about sqrt(.75) times 74. Let us see what that is. It comes out to 64. So H(t) will decline from present 74 and approach 64 from above. This is just what the standard model predicts. Of course we do not know the future.
But going by the standard model, we see that the Hubble distance still has another 15 percent to expand. From the present 13.2 out to 15.3 billion LY.
That means that any photon which can manage to stay within 15.3 billion LY of us, and is heading our way, will eventually make it to us.

It's a nuisance that we seem to be in the midst of changing from 71 to 74 on the Hubble rate. If you want a source on that Ned Wright's news page has the link to the recent paper by Riesz et al. (EDIT, Sylas points out that Riess is spelled ss not sz, and kindly supplies the link to Riess et al 2009)

 

[sylas]

All this discussion assumes we are talking proper distance. Here's where I calculated that 15.3. It's trivial. In the LCDM the energy density eventually goes to 0.75 of what it is today and putting that into the Friedman equations tells what the Hubble rate will be in the limit.

D'oh. Of course. Thanks.

Although, of course, this presumes the equation of state for dark energy is ω=-1, corresponding to a constant density for the vacuum; but since we don't know much about dark energy, that's still up in the air, and another parameter cosmologists are keen to constrain with observations.

Riess et al 2009 give it as -1.12 +/- 0.12, in arXiv:0905.0695v1.

Cheers -- sylas

PS. For readers following along, a caution. The 1.12 here for ω is unrelated to the 1.12 for the event horizon calculated by Chalnoth.

 

[marcus]

I read it is possible for the universe to be expanding faster than the speed of light.
What would be the implications of this?

Some implications (back to the original question):
I'll bet there are many implications that have not yet even been thought through nor even conceived! (let's hope so.)

We are likely able to currently observe only an infinitesimal portion of our own universe...

Naty calls us back to consider the original question. That's good. Chalnoth corrects and sharpens one of the implications which Naty identified.

I get a welcome sense of convergence in this thread, of being on the same page as Sylas says. I will try to confirm and sharpen the implication Naty drew about only seeing a small part.

Of course what we see is a small part if the whole is infinite but suppose the whole is finite--typically then the picture of space is a hypersphere (3D analog of the 2D balloon surface) and it has some definite circumference. The latest WMAP report gives us a lower bound estimate for the circumference of about 600 billion LY, 95 percent confidence.

To examine the source, google "komatsu wmap cosmology" and look at table 2, very near the beginning of the paper. You will get their figure for the radius of curvature, lower bound, in parsecs. Have to convert to lightyears (parsec = 3.26 of those). Of course we are dealing with actual (i.e. proper) distance. If you could freeze expansion it would take a flash of light at least 600 billion years to make the full circle. More precisely the WMAP report's figure comes out more like 630 but I don't want to put to fine a point on it, and say 600.

So to quantify what Naty says, we just have to think about how far we see now, and how far we will ultimately be able to see (which may not be as far as we can now) and compare those horizon distances with, if you like, the half-circumference lower bound of the presentday universe---i.e. 300 billion LY. All we really want is a qualitative impression supporting what Naty said so I'll leave it at that.

The Komatsu et al was published in ApJ early this year, the preprint came out in 2008.
The Riess et al paper with the new Hubble rate of 74 just came out recently. I should get a link.

SHUCKS I've been misspelling Adam Riess's name! And he is one of the heros of the 1998 revolution. Thanks for the link and the correction, Sylas.
I will copy the link for emphasis:
http://arxiv.org/abs/0905.0695

 

[4D-UGRA]

Camilus.
All of this in-fighting is a distraction from your original question. It does appear that space can and does exceed the speed of light. I can only articulate it in simple terms. We have a limited view of the universe. I think, and please correct me if I am wrong everyone, but something like 46.5 billion light-years in all directions. This means that we can not and will not see any light from any further away then that. (lets say 46.5 billion light-years = X) This is due to the fact that at that distance space is moving faster than light (Hubble's law). The how and why, I myself am still sorting out, via these forums and various writings and books. I had a huge problem understanding this myself initially. I have wondered if a serial set of hubble-like telescopes could be positioned throughout space in a line, and if they could broadcast images from beyond this X=46.5 billion light-year visible limit, since at some point the telescopes would pass into their own visible limit and may not be able to see Earth anymore, but could see one to the satilites/telescopes and relay data to that device. Allowing us to break this barrier. Just my Star Trek view of the whole... sorry to interrrupt such productive arguing. (How would you get the devices there and how long would it take etc etc, speed of light etc,)
Do a search on "particle horizon"

 

[marcus]

please correct me if I am wrong everyone, but something like 46.5 billion light-years in all directions. This means that we can not and will not see any light from any further away then that.

Since you ask for whatever corrections we can make, you are talking about the particle horizon and your figure for its presentday distance is old. The new data from the HST published by Riess et al in 2009 would put it at more like 46 flat. If you want to sport three figures, let's call it 46.0.
But that doesn't matter. The main thing you say that is wrong is that we "will not see any light from any further away then that." More light from farther away always coming in. The comoving distance to the particle horizon is increasing at the speed of light. The actual now distance is increasing even faster.
So don't think of the current particle horizon as some fixed final limit.

All of this in-fighting...

All is peaceful now, is it not?

Do a search on "particle horizon"

I have to go. I'll reply more later. It's good to bring up the particle horizon!

It does appear that space can and does exceed the speed of light

EDIT: See Chalnoth's comment in the next post.
I know what you mean though. Just put it in terms of geometry (not "space"). Say it with distances. Distances between observers at CMB rest can increase faster than c.

 

[Chalnoth]

Er, space doesn't exceed the speed of light in any reasonable sense. It doesn't move in a way that is measurable by speed.

 

[yogi]

Camilus.
I have wondered if a serial set of hubble-like telescopes could be positioned throughout space in a line, and if they could broadcast images from beyond this X=46.5 billion light-year visible limit, since at some point the telescopes would pass into their own visible limit and may not be able to see Earth anymore, but could see one to the satilites/telescopes and relay data to that device. Allowing us to break this barrier. "

Unfortunately, that will, in general, not work - take a look if you have access to the Harrison Book "Cosmology" at page 441 The horizon limitation cannot be extended by the farther away telescope sending signals to the nearer telescope

 

[Chalnoth]

Unfortunately, that will, in general, not work - take a look if you have access to the Harrison Book "Cosmology" at page 441 The horizon limitation cannot be extended by the farther away telescope sending signals to the nearer telescope

When you consider that the farther away telescope would send its signal back at the speed of light, and will at best add a small delay in sending said signal, there's no way the signal from the telescope can get back before the photons from the object the telescope is observing get back. So yeah, clearly won't work.

 

[yogi]

I read it is possible for the universe to be expanding faster than the speed of light.

What would be the implications of this?

In the context of the original question posed - the answers have been aimed mostly to academic topics such as how much we can see and how big is the universe. But there are some other issues embraced within the inquiry - for example - if we live in an accelerating universe - will there be any measurable affect upon the gravitational constant - or inertia ...Einstein reasoned that the same Newtonian forces would arise if the universe itself were accelerated rather than the local mass - if that is correct, changes in the expansion rate and changes in the distance at which global acceleration is communicated to local matter may have an influence upon local measurements, at least if one is of a bias that regards the universe as holistic.

 

[Chalnoth]

In the context of the original question posed - the answers have been aimed mostly to academic topics such as how much we can see and how big is the universe. But there are some other issues embraced within the inquiry - for example - if we live in an accelerating universe - will there be any measurable affect upon the gravitational constant - or inertia ...Einstein reasoned that the same Newtonian forces would arise if the universe itself were accelerated rather than the local mass - if that is correct, changes in the expansion rate and changes in the distance at which global acceleration is communicated to local matter may have an influence upon local measurements, at least if one is of a bias that regards the universe as holistic.

The magnitude of the cosmological constant so small that I'm not sure that we'll ever be capable of measuring it.

Granted, scientists are clever, and someday we may find a clever way of measuring this absurdly minuscule effect, but don't bet on it.

 

[Naty1]

Chalnoth posted #24:

(QUOTE]They fact that distant galaxies are expanding at a rate greater than "c" does not mean we can never observer them, only that we can't observe some right now.

Well, no, actually it doesn't mean this...[/QUOTE]

I agree...my wording did not properly express my thought...

Your explanation quoted in post #25 says it a lot better:

objects currently receding up to about 12% higher than the speed of light are emitting photons that we will detect at some point. ...

I had not seen that simple synopsis before...that makes it unambiguous...