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

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1. Jul 26, 2015

### 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)?

2. Jul 26, 2015

### 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.

Last edited: Jul 26, 2015
3. Jul 26, 2015

### 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?

4. Jul 26, 2015

### 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

Last edited: Jul 26, 2015
5. Jul 26, 2015

### 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?

6. Jul 26, 2015

### 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.

7. Jul 26, 2015

### Rupert Young

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

8. Jul 26, 2015

### 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 travelling 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.

9. Jul 26, 2015

### rootone

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

10. Jul 26, 2015

### 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.

Last edited: Jul 26, 2015
11. Jul 26, 2015

### phinds

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

12. Jul 26, 2015

### 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.

13. Jul 26, 2015

### phinds

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

14. Jul 26, 2015

### rootone

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

15. Jul 26, 2015

### Bandersnatch

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.

16. Jul 26, 2015

### 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?

17. Jul 26, 2015

### marcus

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/sinh2/3(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.

Last edited: Jul 26, 2015
18. Jul 27, 2015

### Bandersnatch

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.

19. Aug 2, 2015

### Stephanus

Are you sure?

20. Aug 2, 2015

### Stephanus

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