Agent asks why age of universe is 13.7 billion years. Can anyone help?

[Realitycheck]

How can something achieve 60c? Is this referring to swanson's "aggregate stretching"? Just making sure.

 

If the radius of the known universe is 45 billion LY across and it is expanding at a speed of at least c, then why is the universe only 13.7 billion years old, when mathematically it corresponds to at least 45 billion years old, not counting superfast inflation?

 

Ok, so if the universe was expanding at a speed greater than c, this would explain the discrepancy in measurements. Now, if the universe is expanding at 60c now, that would mean that for most of its life, it was expanding at speeds substantially less than c, in order for the radius to only be 3.5 times the age of the universe.

 

Now time for a technical question. How do we know that the universe is 13.7 billion years old, yet 45 billion year old radius, especially when we cannot see the rest of the universe? Surely some kind of extrapolation. But what if it were bigger than 45 by radius? Would our current calculations and extrapolations disprove this? Are we that sure based on the numbers we have today?

[Martin]

Maybe someone else can help explain this to Agent. We are talking about the LCDM model with certain parameters. That is the model you get, for instance, using Wright's calculator, and it is the model that observational cosmologists typically use these days.

 

It fits the data amazingly well----there are four or five different kinds of data and they keep pouring in and for the past 4 or 5 years they keep confirming the model more and more firmly. The estimates of the main parameters have hardly changed, meanwhile.

 

The model determines the age of the universe at 13.7 billion years, sometimes you see an errorbar or something like 13.66 but it's around that. And the same model mathematically determines the other things I have mentioned, like recession speeds and distances to the CMB source etc. The different numbers are part and parcel of each other, they form an organic whole---all come out of the same model or the same calculator.

 

Of course the age of 13.7 billion fits in with other evidence like abundance of certain star populations, globular clusters and other structure, abundance of isotopes and elements etc. People are always checking to see if the details fit. But the number is what you get out of the LCDM model when you plug in the parameters (71 for Hubble, 0.73 for Lambda, 0.27 for Matter) that represent the observational consensus.

 

Put those numbers in the calculator and you will get that the age is 13.7 billion, and you will also get that the source of the CMB we are now observing is 45.6 billion LY from here.

 

Agent seems to think these two numbers are inconsistent. But not only are they consistent, they DEPEND on each other. You can't change one without changing the other.

 

If you want, put some other parameters besides (71, 0.73, and 0.27) into the calculator and you will get a different number for the age of the universe! But you will also get a different presentday distance for the CMB source.

 

This is kindergarten cosmology, the ratio was always about 3, even back when there were different estimates, and your cosmology professor always pointed this out. Actually a little over 3. And, as you see, 45.6 is a little more than three times 13.7. Ned Wright discusses this in his cosmology tutorial and gives some intuition for it.

 

So heck yes, they are consistent numbers!

 

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

 

BTW I wouldn't call the distance to the CMB source the "radius of the universe".

That is a confusing term for it. A cosmologist would call it the distance to the surface of last scattering.

 

There is also something called the "particle horizon" which is out BEYOND that 45.6 billion LY.

The oldest light comes from the surface of last scattering. The oldest neutrinos come from further off presumably, nearer the actual particle horizon. Neither one is really a good thing to rename "radius of the universe". Better to be more careful with terminology.

[insane_alien]

okay, imagine a length of elastic.

 

on this elastic, there is a object of some description. it can only move with a certain velocity(we'll call it c) relative to the elastic.

we'll anchor one end to make the thought experiment simpler.

 

now, lets have it moving at c away from the anchor point but we'll also stretch the elastic.

while the relative velocity of the object never exceeds c with the elastic it will be c+(some value that depends on time and the distance from the anchor point).

 

to put this in real terms. the anchor point is any conveinient reference frame(like the earth) and the elastic is the space-time continuum.

[Martin]

Alien thanks for stepping in here!

I have some things to add. They may not help Agent individually but they might help others trying to understand.

 

First you simply have to play around with the calculator and put different parameters in and see how they affect the age.

 

Mathematically what's happening is this. the EFE (einst field eqn) describes how geometry changes interacting with matter and there is a simplified form of the EFE called the Friedmann equations which are a differential equation, which the calculator knows how to solve. It knows how to WORK BACK AND RECONSTRUCT THE EXPANSION HISTORY if you tell it paramters describing the present

 

So you tell it 71 for Hubble 0.73 for dark energy or Lambda and 0.27 for matter. 71 tells it how rapidly space is expanding at present

0.27 or matter is important because matter tends to slow down expansion.

and of course the 0.73 Lambda tends to speed it up.

 

and you have to work backwards step by step and see how long before the scalefactor reaches zero! Then that is the age----or how long expansion has been going on. (some models have a bounce and an contraction stage before that, so it is not necessarily the age of the universe, but at least it is how long space has been expanding.)

 

working step by step is exactly what differential equations do! and the Friedmann equation is the basic model in all of cosmology, and Wright's calculator is just running that differential equation. There are a bunch of other online calculators and they produce the same numbers. I know one guy who made his own just for fun---two guys actually.

 

a neat thing is that as you work backwards, space collapses down and that makes matter more concentrated (more stars per cubic lightyear etc...)

so this 0.27 number becomes more important! As you go back you soon reach a time when MATTER IS DOMINANT and overwhelms the expansionary effect of Lambda, do you come to a time when expansion is slowing down.

 

So the calculator goes thru this and basically generates a curve. The curve shows expansion slowing down, but continuing, so that matter thins out, and as it thins out Lambda becomes more dominant and expansion starts speeding up.

 

the same calculation gets you other numbers, like the recession speed for things at various distances----for example the surface of last scattering receding at 60c at the time the CMB light set out on its way to us. And only receding at 3.3 c at present.

 

the same calculation ALSO gets you the age of the universe (or the present expanding phase of it) because all you have to do is follow the expansion history curve back and see where it starts, and how long ago that was!

[swansont]

Put those numbers in the calculator and you will get that the age is 13.7 billion, and you will also get that the source of the CMB we are now observing is 45.6 billion LY from here.

 

Agent seems to think these two numbers are inconsistent. But not only are they consistent, they DEPEND on each other. You can't change one without changing the other.

 

agentchange said "Ok, so if the universe was expanding at a speed greater than c, this would explain the discrepancy in measurements."

 

I think that's a good foundation.

[Martin]

agentchange said "Ok, so if the universe was expanding at a speed greater than c, this would explain the discrepancy in measurements."

 

I think that's a good foundation.

 

It certainly is a good start towards understanding, to recognize that some expansion speeds have to be greater than c.

 

but what is the "discrepancy in measurements" that Agent is talking about?

 

It would make things a lot clearer if Agent could translate his lack of understanding into a QUESTION, or several questions, instead of expressing it by making flat, declarative statements.

 

Also we should point out that it is not true that "the universe was expanding at a speed greater than c"

because there is no one speed of expansion

 

different DISTANCES increase at different rates.

 

we don't know of any one characteristic distance, so the speed of expansion depends on which distance you pick.

 

Yes, at the present time a typical distance would be expanding at some speed greater than c. there are more galaxies outside the Hubble sphere than inside so distances to them are in some sense more typical. but there is no one speed of expansion.

 

Agent still sounds confused. But it is a start, or as you say, a foundation.

[Realitycheck]

Definitely a poor choice of words. I'm overcoming a new shoulder injury, sorry.

 

All is clear to me. My output was garbled. I should probably not even be exerting the output of typing right now, instead resting completely, so that my laziness is not construed as confusion.

 

Obviously, if the universe is not growing at a constant of c, then the universe is not 13.7 bly in radius. Obviously, it grew at a very fast pace for a short period in inflation, somehow much faster than c, and has been growing much slower for the remainder of time, i n order for it to balance out at 3.3 x 13.7 bly.

 

Furthermore, since the universe has been growing at measurable rates for the duration of its life, we should be able to deduce the size of the universe based on these parameters.

[Martin]

Sorry to hear about your shoulder injury, Agent. I notice that in this post you are not asking a question about something in cosmology that you don't understand. You are making declarative statements. So I have the unpleasant job of telling you you are wrong.

 

Here is the main statement that is wrong.

Furthermore, since the universe has been growing at measurable rates for the duration of its life, we should be able to deduce the size of the universe based on these parameters.

 

The trouble is it is based on verbal reasoning instead of familiarity with the math---the actual definitions and the equations. Purely verbal reasoning will usually lead you astray, and it has here.

 

It would be much more fun if you would learn to ask questions about stuff instead of making flat (wrong) assertions that we then have to argue with.

 

the point is that in the usual Friedmann equation model THE SIZE OF THE UNIVERSE IS NEVER DEFINED. what one has is something called the SCALE FACTOR a(t) which the intro to cosmo professor will explain can be thought of as "average distance between galaxies".

It is actually a factor that appears in the metric.

 

The hubble parameter is a'/a the timederivative of a(t) divided by a(t).

 

We have a good handle on a(t) and given measured parameters we can calculate the ENTIRE PAST HISTORY of a(t) back nearly to the start of expansion. That is sometimes called the Expansion History of the Universe.

I have a graph of it if you want the link.

 

But in all of that, the size of the universe is never mentioned. We do not know it. It could easily be infinite. On the other hand if it is finite, this history of a(t) the scale factor does not give it to us. Estimating the size, if it is finite, is a whole other problem.

 

So your statement is wrong. It is a faulty verbal arguement, unfortunately.

We are NOT able to deduce the size of the universe from its growth history---the calculated past history of the scale factor.

 

Of course we can estimate the size of the CURRENTLY OBSERVABLE piece. This is a sphere of current radius around 46 billion LY that contains matter which has sent us light or other signals that we have so far received. Naturally the size of this currently observed piece is constantly growing as time passes and more signals come in. THAT measure of size has been known for a long time and is not of interest.

 

What is of intense interest is to find out if the whole universe is spatially finite and if so what is its real size (not just the piece that happens to be observable at the moment).

 

this is exactly what we can NOT deduce based on knowledge of how the scale factor has grown in the past 13.7 billiion years.

 

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

I have reservations about statements you made in the other part of your post

Obviously, it grew at a very fast pace for a short period in inflation, somehow much faster than c, and has been growing much slower for the remainder of time, in order for it to balance out at 3.3 x 13.7 bly.

 

There are several different scenarios for a split second of "inflation". It has not been established that inflation occurred----or what the physical mechanism could be. Inflation scenarios are speculative, involving exotic matter that has not been observed and does not fit into standard particle physics.

 

It sounds like you are limiting FTL growth to an inflation episode.

 

370,000 years AFTER that supposed split second period of inflation, which is definitely in the POST-inflation period (if inflation occurred at all) you still have the CMB-source matter receding from our galaxy's material at over SIXTY TIMES THE SPEED OF LIGHT.

And there is no mystery how it does that, it is just good old vintage 1915 relativity----General of course----that makes it.

Or if you prefer a solution of the vintage 1923 Friedmann equation that makes it do that, because it comes right out of solving that equation.

 

So we are talking not about Inflation which is comparatively recent and speculative, but about FTL recession speeds that have been known and familiar to cosmologists for over 80 years.

[foodchain]

To Martin:

 

I may be a bit confused but is the current model in cosmology based on general relativity and the standard model? Being the standard explains three of the four known forces in the universe right, and general relativity accounting for the fourth or gravity?

 

As you said in an above post about the current view or model of cosmology being based on what is currently observable would it be safe to speculate that the universe might in fact be hundreds of times larger then what we currently observe if not simply just larger then what we can observe?

 

In regards to the question of age would it just be the physical dynamics of the universe as known in itself to be the physical phenomena used in a model to lead to such a form or size in time? I think this relates to my above two questions and the thread in general.

[Martin]

To Martin:

... is the current model in cosmology based on general relativity and the standard model? ...

 

RIGHT! Cosmology is based on GR. It doesn't even require much particle physics to understand basic cosmology. The underlying theory is GR and there is a simplication of the GR equation called the Friedmann equations which is what cosmologists actually use. Stuff like dark energy and dark matter and regular matter are just numbers that you plug into the Friedmann equations.

 

I put the Fr. eqns in the SFN astronomy sticky thread some years back. they are simple equations describing the growth of the scale factor.

 

You mentioned the Standard Model of particle physics. That is much more complicated and difficult to learn. Basic cosmology is an easy subject that you don't need a lot of prerequisites for.

 

... would it be safe to speculate that the universe might in fact be hundreds of times larger then what we currently observe if not simply just larger then what we can observe?

 

SURE THING! The universe is almost certainly larger than we can ever observe. the presentday estimate of the event horizon is 16 or 17 billion LY. an event that happened today in a galaxy 17 Gly from here we would never get news of. A star 17 Gly from here could explode today and we would never see the flash. No matter how long we wait and no matter how good our telescope. The from the flash would never get here, even given infinite time.

 

We don't know whether the universe is spatially infinite or not. If it is infinite then certainly your estimate of "hundreds of times larger" is safe, and in fact conservative.

 

Personally I suspect the universe will be shown to be finite, in the next few years (at least with high probability) and if I were to take a wild guess I would predict that the circumference will be found to be something like 800 billion LY.

 

the reason we will never be able to see the whole thing no matter how long we wait is because of expansion. Light from half a circumference away will never be able to reach us, because of expansion, in no matter how long a time. This is according to the prevailing mainstream model (finite LCDM)

 

 

 

In regards to the question of age would it just be the physical dynamics of the universe as known in itself to be the physical phenomena used in a model to lead to such a form or size in time? I think this relates to my above two questions and the thread in general

 

It sounds like you are asking an extremely interesting question to which i don't know enough to answer completely. there are things you can measure like the presentday hubble parameter and the presentday matter density and a spatial curvature number called Omega. No curvature means Omega = 1. Slight positive curvature means Omega in the range [1.01, 1.04].

The map of the CMB helps determine the curvature. Also counting the numbers of galaxies at different redshifts.

With these three numbers one can run the model back and learn the age!

 

But then one should check and see if that age calculated from the model is reasonable----did it leave enough time for stars and galaxies and stars to form? Did it give enough time for the generations of stars where the first generation didn't have heavy elements but MADE them in supernovae and gave them to the next generation, etc. Do the small slowburning stars seem to be the right age for it to fit consistently?

 

Astronomers always try to come at everything from many different angles and check everything out over and over.

 

For me the most interesting is how they measure Omega. If it really is some positive number like 1.01 then the universe is spatial finite with a circumference of about 800 billion LY. If it is 1.02 then it is smaller, because more curved, and so on. In January Ned Wright gave what he called the "bestfit" estimate of 1.011. But he also said he could not rule out the flat case of exactly 1, which would mean spatial infinite.

 

Estimates of age of universe will probably not change very much any more. the more data comes in the more it confirms 13.7 or thereabouts

but more data will certainly refine the estimates of Omega, and narrow down the errorbar (which is now 68 percent [1.010, 1.041]

so the SIZE figures may change in the coming years, but probably not the AGE figures. That is just my guess---very IMHO.