I How big and how old is the Universe?

[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.

 

[phinds]

If the visible universe began as a single dot

It did not. This is pop-sci nonsense.

If it's 13.7 billion light years across that's partly due to inflation.

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.

 

[Chalnoth]

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.

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.

 

[Bandersnatch]

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?

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.

 

[GeorgeDishman]

the value of Hubble parameter measured today must have been larger in the past.

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.

 

[Bandersnatch]

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.

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.

 

[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?

 

[phinds]

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?

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.

 

[Bandersnatch]

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?

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)

 

[phinds]

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)

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.

 

[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.

 

[Bandersnatch]

Yes, every comoving observer.

 

[phinds]

Yes, every comoving observer.

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]

 

[Bandersnatch]

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

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?

 

[phinds]

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?

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.

 

[GeorgeDishman]

every comoving observer measures the same age of the universe, so where's the issue

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

 

[Bandersnatch]

oh you nitpicky bastards

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

 

[phinds]

oh you nitpicky bastards

Ah, high praise indeed for us nitpicky bastards.

 

[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.

 

[GeorgeDishman]

20 billion light years away measuring the size and age 10 billion years ago?

Any message an alien cosmologist sent us 10 billion years ago will be 10 billion years out of date

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

 

[windy miller]

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.

13.8 billion years since the big bang. But we don't 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

 

[phinds]

13.8 billion years since the big bang. But we don't know that the big bang was really the beginning of the universe.

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.

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 ...

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

 

[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

 

[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)?

 

[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.

 

[GeorgeDishman]

I was taking as an example an alien who lived beyond our present light cone. Tweaking Cosmocalc for a lookback time of 10 billion years, I get a redshift of z=1.719 as you said so if the alien astronomer was 20 billion light years away at that time, that gives a comoving distance of 20*(1+1.719) or 54.38 billion light years. Light from that galaxy has not reached us yet, but I expect it is still close enough that it will do so in the future. However, I can't see a way to use cosmolcalc to tell me when that light will reach us.

 

[Bandersnatch]

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

No, as the paper says, based on the uncertainty in the observable curvature of the universe, you can fit at least 251 observable universes in a universe that is closed, but whose curvature is low enough to be hidden in the error bars. It looks like they're using WMAP5 or 7 data. With most recent PLANCK data you'd get a larger radius of curvature and a correspondingly higher number of patches of observable universe fitting into the larger whole.
For some reason the paper incorrectly uses the term 'Hubble sphere' to describe the observable universe size (distance to the last scattering surface).

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

I don't see any obvious way to do it. Maybe @Jorrie can help?

In the meantime, you could use these graphs:

and (if the gif doesn't work, just go there:)
http://yukterez.net/lcdm/i.html#plot
http://yukterez.net/lcdm/lcdm-flrw-animation.gif

 

[phinds]

No, as the paper says, based on the uncertainty in the observable curvature of the universe, you can fit at least 251 observable universes in a universe that is closed, but whose curvature is low enough to be hidden in the error bars. It looks like they're using WMAP5 or 7 data.

Thanks. I've seen numerous estimates of minimum size for the U relative to the OU and they have been all over the map. I think the biggest was something like 10E500 or so. Was not aware of the one you quote and don't recall having seen any that small. I'm quite amazed that it could BE that small.

 

[PeterDonis]

Our past light cone only extends back to the surface of last scattering at z=1089

More precisely, the portion of our past light cone which is visible using EM radiation only extends back to the surface of last scattering. But the actual past light cone itself extends back beyond that--we just can't observe that portion directly with EM radiation (though we can obtain evidence about it in other ways).

 

[GeorgeDishman]

I did a search of one of the forums a few weeks ago and found an old post (but I can't find it now of course) that gave the radius of the 3-sphere as:

$R = c / (H_0 sqrt(Ω_K))$

Plugging in the upper limit for $Ω_K$ from the Plank 2015 results then gives a minimum total volume. However, I've seen other sites that use that same argument but get very different numerical values from what I worked out.

 

[Bandersnatch]

I did a search of one of the forums a few weeks ago and found an old post (but I can't find it now of course) that gave the radius of the 3-sphere as:

$R = c / (H_0 sqrt(Ω_K))$

Plugging in the upper limit for $Ω_K$ from the Plank 2015 results then gives a minimum total volume. However, I've seen other sites that use that same argument but get very different numerical values from what I worked out.

You should get the minimum radius of the curvature approx R=205 Gly. Is that what you have?

 

[GeorgeDishman]

You should get the minimum radius of the curvature approx R=205 Gly. Is that what you have?

Yes, for a Hubble Length of 14.4 Gly from Wikipedia: $R = 14.4 / \sqrt(0.005) = 203 Gly$ for the radius, which I think means $2 \pi R = 1280 Gly$ for the circumference (proper distance to return to your starting point) and $2 \pi ^2 R^3 = 1.67*10^6 Gly^3$ total volume. The Planck value is 95% confidence (from memory) so that would be 97.5% confidence minimum limits (50% chance of curvature < 0) assuming a 3-sphere rather than some other topology.

I found the other similar calculation I saw recently by Ethan Siegel in a blog (obviously not an authoritative source) but that seems to be a factor of 10 larger:

"If the Universe does curve back and close on itself, its radius of curvature is at least 150 times as large as the part that’s observable to us! Meaning that — even without speculative physics like cosmic inflation — we know that the entire Universe extends for at least 14 trillion light years in diameter, including the part that’s unobservable to us today."

http://scienceblogs.com/startswithabang/2012/07/18/how-big-is-the-entire-universe/

 

[GeorgeDishman]

In the meantime, you could use these graphs:

Thanks, I recognise those from the Lineweaver paper. The example I gave is outside our cosmological event horizon so the light will never reach us.

 

[Bill McKeeman]

I do not think we have any evidence of what an observer somewhere else in the Universe would see. You must be applying the Cosmological Principal, which is an assumption, not a fact.

 

[PeterDonis]

I do not think we have any evidence of what an observer somewhere else in the Universe would see.

Sure we do; everything we can see is evidence about what observers elsewhere in the universe would see. It's not perfect evidence, but it's not no evidence either.

 

[rootone]

I do not think we have any evidence of what an observer somewhere else in the Universe would see. You must be applying the Cosmological Principal, which is an assumption, not a fact.

I'd say it's a reasonable assumption though, given that all of the Universe which we actually do see, is in fact isotropic and homogeneous at the large scale