How can the observable universe be 46 billion lyrs in size?

[Rupert Young]

I watched a BBC documentary that said that the observable universe is about 46 billion light years in size. How can this be if the age of the universe is 13.7 billion years (and nothing travels faster than the speed of light)?

 

[rootone]

Because (according to observations and the best theories we have), the observable Universe is expanding.
The most distant parts of the visible universe appear to be receding from us at approaching light speed, and there is good reason to believe that there is more universe beyond what is observable, and that could be receding even faster than light speed.
Light speed does not limit the rate of space expansion it is only a limit for objects which have mass and which are moving through space in relation to other objects.

 

[Rupert Young]

If we can observe something is 46 billion light years away doesn't that mean that the light took 46 billion years to travel from there to here. How can that be if the universe is only 13.7 billion years old?

 

[rootone]

The light from a very distant object which is being observed, (a quasar let's say) was emitted not too long after the 'big bang, some 13.7 billion years ago.
Due to the expansion of space the object is now much further away.
Note that while getting more distant the object has not traveled THROUGH space

 

[Rupert Young]

Doesn't that mean then that that light has traveled faster then the speed of light? I.e. it has traveled 46 billion light years in less than 13.7 billion years?

 

[rootone]

No, Light always travels at the speed of light.
The light of an observed very distant object was emitted 13+ billion years ago, and that light is what we see.
If the object is still in existence it is now much further away than it was then, and any light it emits would take longer to reach us.

 

[Rupert Young]

The light of a very distant object was emitted 13+ billion years ago, and that is what is observed by us.

If it is observed at 13 billion why is it said that the observable universe is 46 billion?

 

[Bandersnatch]

A good analogy here is that of an ant walking on a rubber band that is being stretched.

Imagine two points, A and B, on the rubber band, 100 cm distant. The ant walks from A to B at a constant speed of 1 cm/s.

On a static band (= a non-expanding universe), it would take it 100 seconds to cover that distance.

If the rubber band is being stretched (=an expanding universe), then it'll take more than 100 seconds to get from A to B at the same, constant speed, since as the ant walks there will be more and more distance for it to cover.
What's more, by the time the ant reaches point B, point A will have receded to a distance larger than both the initial distance, and the distance you'd get from multiplying the ant's velocity times the time of travel.

This means that unlike in the static example, there are three distances that we need to consider in an expanding universe:
-the distance between the source and the observer at the time of emission of a signal
-the distance 'covered' by the traveling signal (i.e., light travel time, or speed of the signal times elapsed time)
-the distance between the source and the observer at the time of reception of the signal

For the oldest observable signal (the cosmic microwave background radiation) the first is about 44 million light years, the second is 13.7-ish billion light years, and the third is about 46 billion light years.

 

[rootone]

The wiki article is worth a read.
https://en.wikipedia.org/wiki/Observable_universe

The best estimate of the age of the universe as of 2013 is 13.798±0.037 billion years[5] but due to the expansion of space humans are observing objects that were originally much closer but are now considerably farther away (as defined in terms of cosmological proper distance, which is equal to the comoving distance at the present time) than a static 13.8 billion light-years distance.[8] It is estimated that the diameter of the observable universe is about 28 gigaparsecs (93 billion light-years, 8.8×1026 metres or 5.5×1023 miles),[9] putting the edge of the observable universe at about 46–47 billion light-years away.

 

[Chronos]

We can only view objects at the distance they were when the photons we detect were emitted. Imagine photographing a car at a distance of 100 meters that is speeding away from you at 100 metersper secondr. Judging by the picture the car was 100 yards distant when the picture was taken. That does not reflect the fact th car actually 200 meters distant at when you view the photo one second after it was taken. In this case you cannot view your picture of the universe until 13.7 billion years later.

 

[phinds]

The most distant parts of the visible universe appear to be receding from us at approaching light speed ...

This is incorrect. The most distant parts of the observable universe are receding from us at about 3c

 

[rootone]

Yes I agree, if the most accepted theories of expansion are accurate they would have to be receding from us NOW at that sort of velocity.
I meant that any light which we can see must have been emitted at a time when their rate of recession was less than c.

 

[phinds]

Yes I agree, if the most accepted theories of expansion are accurate they would have to be receding from us NOW at that sort of velocity.
I meant that any light which we can see must have been emitted at a time when their rate of recession was less than c.

Fair enough. Wording can lead to confusion on the whole issue of "now" and "then" and distances on cosmological scales.

 

[rootone]

It can, and as well, 'relativity of simultaniety' hurts my brain when thinking about this kind of thing.

 

[Bandersnatch]

I meant that any light which we can see must have been emitted at a time when their rate of recession was less than c.

It's not true though. The the changing rate of expansion allows for signals emitted from beyond the Hubble sphere to be observed.

Have a look at this paper:
http://arxiv.org/abs/astro-ph/0310808
it might clear up things a bit.

 

[rootone]

I can see that a changing rate of expansion would allow for this.
Yes I had forgotten that in the most accepted model. not only is the observable universe expanding, but the rate of expansion is accelerating.
I'll take a look at the arxiv link.

Is there considerable consensus regarding the profile of the changing expansion rate?
This must make a difference for the very long term future of the Universe.
Accelerating expansion seems to make the cyclic models unlikely, but both of 'heat-death' or an eventual 'big-rip' are still plausible?

 

[marcus]

If we can observe something is 46 billion light years away doesn't that mean that the light took 46 billion years to travel from there to here. How can that be if the universe is only 13.7 billion years old?

Here is how far a photon can have traveled since year 173,000----that is 0.00001 zeit. We work in zeit time units since more convenient.
$$\int_.00001^.8\frac{1.3}{sinh^{2/3}(1.5t)}cdt$$

t=0.8 zeit is the present age. cdt is a little step the light takes around time t.
And 1.3/sinh^2/3(1.5t) is the factor by which that little step gets expanded between time t and the present. So the integral obviously gives how far the light is today from where it originated.
If you evaluate the integral you get 2.64 lightzeit. Multiply 2.64 by 17.3 billion lightyears to get the distance in that unit. You will get around 46.

That is the RADIUS of the currently observable region surrounding us. Light coming in today from the most distant matter can have traveled about that far with the help of expansion. A little farther if you give it the first 173,000 years as well. But I like to use 0.00001 zeit as a cut-off because the integrand becomes less precise close to the start of expansion.

To evaluate the integral, if you care to, go to
http://www.numberempire.com/definiteintegralcalculator.php
for the integrand, type in 1.3*(sinh(1.5*t))^(-2/3)
type in t for the variable
and .00001 and .8 for the limits of integration, and press "calculate"
You will get 2.64, that means 2.64 lightzeit which translates to around 46 billion lightyears.

 

[Bandersnatch]

Is there considerable consensus regarding the profile of the changing expansion rate?
This must make a difference for the very long term future of the Universe.
Accelerating expansion seems to make the cyclic models unlikely, but both of 'heat-death' or an eventual 'big-rip' are still plausible?

You'll find evolution curves for the concordance model (ΛCDM) in that paper I linked to earlier (fig.1). It's over ten years old, but still valid.

For the long-term, big rip is unlikely as the dark energy appears to be in the form of the cosmological constant (i.e., doesn't change in time, constant per unit volume). It still might turn out to be otherwise - the results are fresh and by no means iron-clad. The concordance model assumes cosmological constant, and heat death is the most likely end-scenario there.

I don't know much about cyclic models. As far as I understand they're all purely speculative (no measurable predictions so far). They all have one way or another devised to get to the oscillation from heat death or big rip.

 

[Stephanus]

The most distant parts of the visible universe appear to be receding from us at approaching light speed, and there is good reason to believe that there is more universe beyond what is observable, and that could be receding even faster than light speed.

Are you sure?

 

[Stephanus]

This is incorrect. The most distant parts of the observable universe are receding from us at about 3c

At 3c?? More than speed of light.
Because of this equation $\text{age} * 1.3 * sinh(1.5 * t)^{\frac{-2}{3}}$?

http://www.numberempire.com/definiteintegralcalculator.php

What you put in for "function to be integrated" (I'll explain why later) is 1.3*(sinh(1.5*t))^(-2/3)
and because the variable is t you change x to t in the variable box
and for the limits you put in 0.00001 and 0.8

If you want the answer directly in billions of LY you can instead put in 17.3*1.3*(sinh(1.5*t))^(-2/3)

 

[Stephanus]

This means that unlike in the static example, there are three distances that we need to consider in an expanding universe:
-the distance between the source and the observer at the time of emission of a signal
-the distance 'covered' by the traveling signal (i.e., light travel time, or speed of the signal times elapsed time)
-the distance between the source and the observer at the time of reception of the signal

For the oldest observable signal (the cosmic microwave background radiation) the first is about 44 million light years, the second is 13.7-ish billion light years, and the third is about 46 billion light years.

Perhaps my question is ridiculous, but...
So the light that we receive from cmb is when the cmb WAS 44 millions ly away from us?
But it takes 13.7 billions years (not ly) for the signal to reach us.
Now, that cmb is 46 billions ly away from us.

 

[Stephanus]

This is incorrect. The most distant parts of the observable universe are receding from us at about 3c

I"m sorry. If you said that the most distant parts are receding 3c from us. Then...
I once watched a youtube video that Brian Greene? (perhaps others, but they would come up with the same conclusion) says that in the far future, the only galaxy that we (our descendant, if we can survive that long ) can see is Milky Way (or Andromeda - Way?, they'll surely hit us, or we hit them) because the other galaxies are receding faster from us more than c.
I don't know if my "imagination" is correct or the techinical detail is correct.

A good analogy here is that of an ant walking on a rubber band that is being stretched.[..]

No matter how fast the galaxies are receding from us, we CAN STILL see the light can't we? I imagine Hubble Law, 70km/s per megaparsec.
Or 70 km/s per 3 million ly;
70 m/s per 3000 ly
70 mm/s per 3 ly
or 350 nano meter per 1000 AU
So?
Even if it recedes away from us more than c. The light still tries to get to us. And every 1 AU it jumps 350 pico meter and getting closer and closer. Can't it reach us? Is Brian Greene wrong?

 

[Bandersnatch]

Perhaps my question is ridiculous, but...
So the light that we receive from cmb is when the cmb WAS 44 millions ly away from us?
But it takes 13.7 billions years (not ly) for the signal to reach us.
Now, that cmb is 46 billions ly away from us.

Not a dumb question at all. That's exactly right.

No matter how fast the galaxies are receding from us, we CAN STILL see the light can't we? I imagine Hubble Law, 70km/s per megaparsec.
Or 70 km/s per 3 million ly;
70 m/s per 3000 ly
70 mm/s per 3 ly
or 350 nano meter per 1000 AU
So?
Even if it recedes away from us more than c. The light still tries to get to us. And every 1 AU it jumps 350 pico meter and getting closer and closer. Can't it reach us? Is Brian Greene wrong?

The 70 km/s/Mpc translates to the recession velocity equal to c at about 14 Gly. If the expansion rate were constant, this would mean that nothing emitted from beyond that point could be ever observed - for every 1 ly the signal would cover every year, there would be 1 ly more of distance to cover.
But the expansion rate has been changing throughout the history of the universe, with the Hubble constant going steadily down and asymptotically towards even lower value than today's. So light that initially might have found itself unable to approach, eventually managed to start getting closer.

 

[phinds]

At 3c?? More than speed of light.
Because of this equation $\text{age} * 1.3 * sinh(1.5 * t)^{\frac{-2}{3}}$?

I have no idea what that equation is, but yes, 3c. There is no speed limit on recession speed.

 

[Stephanus]

Not a dumb question at all. That's exactly right.The 70 km/s/Mpc translates to the recession velocity equal to c at about 14 Gly. If the expansion rate were constant, this would mean that nothing emitted from beyond that point could be ever observed - for every 1 ly the signal would cover every year, there would be 1 ly more of distance to cover.
But the expansion rate has been changing throughout the history of the universe, with the Hubble constant going steadily down and asymptotically towards even lower value than today's. So light that initially might have found itself unable to approach, eventually managed to start getting closer.

Yes, they can't reach us. I have imagined that. The travel 1 ly, space expands 1.1 ly. Another 1 ly, another 1.1 (perhaps more, because the distance is farther 0.1 ly, and on and on) It will never reach us.

 

[Bandersnatch]

Yes, unless you allow for the Hubble constant to go down with time - which it has been doing.

 

[Stephanus]

Yes, unless you allow for the Hubble constant to go down with time - which it has been doing.

And...?
What if the Hubble constant go down even <0?
The big crunch?

 

[Stephanus]

Yes, unless you allow for the Hubble constant to go down with time - which it has been doing.

https://en.wikipedia.org/wiki/Hubble's_law#Observed_values
Are these numbers re-correction or it is actually decreasing?

 

[marcus]

Yes, unless you allow for the Hubble constant to go down with time - which it has been doing.

Just to illustrate what Bander said. In the standard cosmic model the Hubble rate H(t) is always declining but is beginning to kind of level out. This plot shows the history of H up to the present (which is t=0.8 on this scale) and then on into the future.

And the plot shows the history of a photon which is heading towards us since very early times, but is at first swept back by expansion, until around t=0.234, and then since H declines enough, it begins to make progress.

The photon is the red curve. It arrives here at the present day (t = 0.8) and then goes on past us into the future.
the blue curve is the Hubble radius, it is essentially the reciprocal of the Hubble rate--one over H. So it has been increasing as H decreases, and will continue to increase (according to standard cosmic model).

 

[Bandersnatch]

And...?
What if the Hubble constant go down even <0?
The big crunch?

It looks like we live in a universe with the cosmological constant, so the Hubble constant will not go zero, but to a specific non-zero value (63 km/s/Mpc, iirc), and the universe will keep on expanding.
What it means, though, is that there will always be a bit more of the universe to observe - we'll always be seeing more and more redshifted photons from farther and farther distance, even if the total volume of observable universe is finite (we'll never see farther than 63 Gly by today's measure).

The pre-dark energy models included scenarios where H went down asymptotically to zero (the universe has just the right amount of matter to stop the expansion and not recollapse), as well as big crunch models where matter content in the universe reverses expansion.
These are now obsolete.

https://en.wikipedia.org/wiki/Hubble's_law#Observed_values
Are these numbers re-correction or it is actually decreasing?

Those numbers are refinements of $H_0$ - the Hubble constant at present time.
To see the evolution of Hubble constant you need a graph plotting H against redshift (or time, or distance).
Such as this one:

(never mind the error bars. You can read more about it in the paper: http://arxiv.org/abs/1011.5000)

(and I see marcus was faster this time! :) )