# I How big and how old is the Universe?

1. Nov 17, 2016

### wwoollyyhheeaa

If the visible universe began as a single dot and inflated in a very short time then its size as measured from standard candles and red shifts would presumably give us its present size and speed of regression. But its age wouldn't be the same number of years as the number of light years of its size, would it? If it's 13.7 billion light years across that's partly due to inflation. not only expansion. I'm told that if we project the size versus time graph back to a dot at the origin we get the wrong answer for the age of the universe because the expansion isn't the only factor to take account of, is it? Can someone please explain/deny/confirm this.

Last edited: Nov 17, 2016
2. Nov 17, 2016

### phinds

It did not. This is pop-sci nonsense.
It is not. This is a misconception on your part. The AGE is 13.7 billion years but it has been expanding and the O.U. is now about 98 Billion LY in diameter.

3. Nov 17, 2016

### Chalnoth

It is possible to project backward in time to when our mathematical models say the universe was a dot. The models do do this make use of measurements of the matter/energy density of our universe combined with the current expansion rate, and extrapolate backwards in time. The expansion over time is what we need to make use of to find this "dot", but that expansion over time can't be directly observed for the entire history of our universe, and must be inferred from other measurements.

Extrapolating backwards all the way to the dot (formal term: singularity) isn't a valid thing to do, though: the singularity is mathematical nonsense, and can't describe reality. Instead, there had to be some physics beyond the current standard model that describes whatever event happened at around the time our (incomplete) models say there was a singularity. There are a number of proposals for this, e.g. inflation, a bounce in loop quantum cosmology, the ekpyrotic model, as well as a number of even more elaborate models.

4. Nov 17, 2016

### Bandersnatch

Have you by any chance heard this in a first lecture of an intro cosmology course, or in an intro astronomy course? Because it sounds like the first thing that is done after showing the Hubble law.

One begins with describing the Hubble law V=Hd, treats the current values of all velocities as if they were constant in time - i.e. as if the Hubble parameter was changing like 1/a (where a is the scale factor), and what is noticed is that when extrapolating backwards the time for all distances in the universe to get to 0 size equals 14.4 billion years*.

In other words, a coasting cosmology in an empty universe is described, where the only thing that matters is the initial expansion impulse.

Then a note is made that the assumption used in this calculation - that of the velocities being constant in time - is incorrect, since the universe is filled with matter and radiation whose mutual gravitational attraction slows down the initial expansion impulse, hence the value of any recessional velocity must have been larger in the past than is measured today. This translates to the value of the Hubble parameter falling faster than 1/a.
Additionally, the universe contains dark energy, which in turn acts to push everything apart, which provides another modification to the way the H changes.

So the final note should be that the simplest extrapolation one can make cannot be correct, and furthermore, the fact that you do get from it the age of the universe that is quite close to the actual value obtained from a detailed model - is (literally) a cosmic coincidence.

*how? - Hubble law states $V=H_0 d$, and $V=d/t$, so $d/t=H_0 d$, and $t=1/H_0$. Where $H_0$ is the current value of the Hubble parameter. This is called the Hubble time.

Last edited: Nov 18, 2016
5. Nov 18, 2016

### GeorgeDishman

Can I be a grammatical nitpicker and suggest "the value of Hubble parameter must have been larger in the past than is measured today.", sorry.

6. Nov 18, 2016

### Bandersnatch

Heh, yeah. Looking at it again, it doesn't make much sense. And here I thought I had a reasonably good grasp of the language ;) . Cheers.

edit: aand I've found some more substantial errors in there as a result of reading it again. Now hopefully all corrected.

Last edited: Nov 18, 2016
7. Nov 18, 2016

### wwoollyyhheeaa

I see. Thanks. Just one more question if I may. If the universe is 98 BLY across, where are we in relation to the edges? And if we take the ratio distance/time we should get speed. But the ratio is 98/13.7 = 7.15 with no units. Why don't we get units?

8. Nov 18, 2016

### phinds

The universe is NOT 98 BLY across, it is of indeterminate size but the consensus is that it is a huge number of orders of magnitude larger that the OBSERVABLE universe, which IS 98 BLY across and is centered exactly at the bridge of your nose. And Mine.

9. Nov 18, 2016

### Bandersnatch

The 45-ish Gly is the radius (and 98-ish is the diameter) of the observable universe in terms of proper distance - it's where the farthest objects that we can see (the CMBR) are now (as opposed to where they were when they emitted the radiation we see). It is always centred on the observer, and is the same for any observer - i.e., no matter where you are in the universe, you see the observable universe as extending to 45 Gly in every direction.
This has nothing to do with the size of the universe as a whole, of which we know precious little - it could be infinite or finite but curved upon itself, but actual physical 'edges' are not considered a possibility.

You won't get any meaningful speed from such calculations as you've presented since the maths is more complicated (although in this particular case these are of course units of speed: distance/time, i.e. billions of light-years/billions of years, => light-year/year => c)

10. Nov 18, 2016

### phinds

Just to clarify for the OP, it is NOT "the same for any observer" it is DIFFERENT for every observer but it is the same SIZE for every observer.

11. Nov 19, 2016

### GeorgeDishman

It should also pedantically be qualified to say it is the same size for every observer who measures the same age for the universe.

12. Nov 19, 2016

### Bandersnatch

Yes, every comoving observer.

13. Nov 19, 2016

### phinds

Not quite. @GeorgeDishman has it right. Think about it.

[I'm assuming the normal definition of comoving, i.e. comoving wrt the CMB, meaning no moving wrt the CMB, which is not a requirement of George's statement]

14. Nov 19, 2016

### Bandersnatch

Thinking might be hard in my present sodden state, but bear with me - every comoving observer measures the same age of the universe, so where's the issue?

15. Nov 19, 2016

### phinds

If you and I are NOT comoving but measure the universe as the same age then we are moving at the same speed wrt the CMB so we are not comoving but we do have the same size OU.

That is, you covered a single case, he covered all cases.

16. Nov 19, 2016

### GeorgeDishman

What about an alien astronomer in a comoving galaxy 20 billion light years away measuring the size and age 10 billion years ago?

17. Nov 19, 2016

### Bandersnatch

oh you nitpicky bastards

You're both right, of course. One needs to take pains to keep the wording precise.

18. Nov 19, 2016

### phinds

Ah, high praise indeed for us nitpicky bastards.

19. Nov 19, 2016

### Chronos

Any message an alien cosmologist sent us 10 billion years ago will be 10 billion years out of date and suggest a ridiculously [from our POV] small universe.

20. Nov 20, 2016

### GeorgeDishman

It will be a lot more out-of-date than that by the time it gets here (he said, being nitpicky again).

21. Nov 20, 2016

### windy miller

13.8 billion years since the big bang. But we dont know that the big bang was really the beginning of the universe. Many proposals for quantum gravity imply the universe existed before the big bag So the universe is of unknown age and of unknown size. Its at least 13.8 bio years old and at least 251 times the size of the observable universe but could be way bigger than that, possible infinitely large and infinitely old. Nobody knows the age of the universe or its size, we can just put minimums on both.
https://arxiv.org/PS_cache/arxiv/pdf/1101/1101.5476v1.pdf [Broken]

Last edited by a moderator: May 8, 2017
22. Nov 20, 2016

### phinds

Agreed, but it IS the age of the temporal part of the universe that we are likely to ever be able to know anything about.

I think you likely mean 10E251, not 251, yes?

23. Nov 20, 2016

### Chronos

For an observer at a comoving distance of 20 billion light years, that observers universe would be appear to be age 3.79 Gy [IOW 10 billion years younger than its present age of 13.79 Gy]. Bear in mind that light travel time can never exceed the age of the universe, for obvious reasons. So, if you see a galaxy at a commoving distance of 20 billion light years, which we do all the time, [redshift = 1.72], it has a look back time of just a hair over 10 billion years. That is how long that light [message] needed to reach you. Math courtesy of Jorrie's cosmo calculator - re: http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc_2013.htm

Last edited: Nov 20, 2016
24. Nov 21, 2016

### GeorgeDishman

My error this time, my statement was ambiguous. For a redshift of 1.72, the lookback time is ~10 billion years but the proper distance of the source at that time was just 5.84 billion light years. The arbitrary 20 billion years I picked would be 3.42 times farther away. I should have made clear I meant distance then, not distance now.

Incidentally, can cosmocalc provide a prediction of when light from such an object, beyond our past light cone, would eventually reach us (if ever)?

25. Nov 21, 2016

### Chronos

We need to be careful about distances here. A comoving distance of 20 billion light year corresponds to a redshift of 2.64 based on the latest planck data for Ho. The age of the universe at z=2.64 is 2.47 Gy with a look back time of 11.32 Gy. So, the age of the universe for an observer viewing the universe at a comoving distance of 20Gy is only 2.47Gy [a look back distance of 11.32 Gy]. A view of the universe with a look back time of 10 Gy corresponds to a comoving distance of 15.9Gy, not 5.84 Gy. That is the proper distance to the source at the time the now z=2.64 photons were emitted. Our past light cone only extends back to the surface of last scattering at z=1089, which is currently observable. We cannot see any further because the universe was EM opaque prior to that time.