## / Age of the Universe

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I was watching the BBC cosmology programmes with Brian Cox a few weeks ago and he described how to estimate the age of the universe by using the rate of the universe's expansion (75km/s/MParcsec).

If something had travelled from Earth at 75km/s for about 13 billion years, then it would be about 1 MParsec away now. Which was the basis of the calculation that concludes that the universe is 13 billion years old.

But, it seems to me now that this is purely a coincidence. A point in space that is now 1 MParsec away has not been moving away at a constant 75 km/s. When it was closer, it would have been moving more slowly.

Finally, if the universal expansion is constant (75km/s/MP), then the calculation will give a constant 13 billion years regardless of how old the universe is.

Are there any physicists who can explain this?

I'm not sure I fully understand your question, however: In getting from the current value of the Hubble constant (as you say, around 72 km/s/Mpc) to the age of the universe, one does take into account how the expansion rate has changed over time. One can do that because, given the constituents of the universe, one can calculate how the expansion rate will have changed (e.g. gravity slowing things down).

> Finally, if the universal expansion is constant (75km/s/MP), then the calculation will give a
> constant 13 billion years regardless of how old the universe is.

I'm not sure I understand the question. Given an expansion rate, one then runs things backwards in time to predict the time when all lengths were zero, so everything was in the same place. This was the Big Bang and the beginning of our universe. Thus the current expansion rate and the time since the Big Bang are intimately related.

>
> Finally, if the universal expansion is constant (75km/s/MP), then the calculation will give a constant 13 billion years regardless of how old the universe is.

I don't fully understand this malarkey but isn't the accepted theory that the expansion is accelerating. Not sure how this effects your calculation.
it is postulated that the expansion of the universe has remained relatively constant after the initial inflation depending on who's model you believe. But to be totally fair cosmology is 96% fudge anyway.

>
> I'm not sure I fully understand your question, however: In getting from the current value of the Hubble constant (as you say, around 72 km/s/Mpc) to the age of the universe, one does take into account how the expansion rate has changed over time. One can do that because, given the constituents of the universe, one can calculate how the expansion rate will have changed (e.g. gravity slowing things down).

hmmm how can you calculate the change in expansion rate when you don't know what most of the universe actually is?
In reply to subalpine: its not so much the expansion of the stuff your worried about its the expansion of the space in between the stuff so it doesn't really matter what the stuff is?

if that makes any sense?

> ... it is postulated that the expansion of the universe has remained relatively constant after the
> initial inflation depending on who's model you believe.

Well no (unless you're taking a very lax interpretation of "relatively constant"), it's more that the changes in expansion rate are factored in to the calculation.
to be fair the hubble constant is one of the least precisely known constants around, its been believed to be fairly much anywhere between 50-100 with differing sizes of error bars over the last decade or so. We've sort of met in the middle somewhere.

my point still stands though cosmology is mostly fudge, rum and rasen where the stuff we know is the rasens and most of the rest of it is fudge

> hmmm how can you calculate the change in expansion rate when you don't know what most of the universe actually is?

We do know quite a bit about how the stuff behaves, even if we don't fully understand it. You can actually trace out the expansion of the universe by looking at very distant objects (supernovae) which, since they are very distant, we observe as they were eons ago, and thus we can see the universe as it was when much smaller. Thus the expansion rate over time is an observed quantity.

> its been believed to be fairly much anywhere between 50-100 with differing sizes of error bars over the last decade or so.

That's not true, it's been pretty settled for longer than a decade. If you'd said 4 or 5 decades then you'd have been ok.

> my point still stands though cosmology is mostly fudge ...

Not true, there is plenty of strong evidence for the claims being made.
In reply to Coel Hellier: one thing is constant- the 'standard candles' eg type 1 supernovas;)
well, apart from the one's that aren't:
http://arxiv.org/abs/astro-ph/9805201

*popcorn*

Some dispersion in SNe luminosities is known and accounted for. What is your point? Cosmologists are well aware of the limitations of their data, where there are limitations.
didn't say there wasn't evidence, just not as much as people in any other field would call enough. If I tried to do my star formation research with as much knowledge as cosmologists have id be pretty stuck.
In reply to Coel Hellier: are type 1a variations factored in to the age of universe error estimate?

> are type 1a variations factored in to the age of universe error estimate?

Yes. Anyhow, much of the constraint on the age come from fluctuations in the microwave background, which are independent of SN1as. There are now several independent lines of evidence all leading to the same result.

> If I tried to do my star formation research with as much knowledge as cosmologists have id be pretty stuck.

I'm willing to bet that Hubble's constant and the age of the universe are known to better accuracy than the mass-radius relation of an M dwarf.

With the CMB results totally backing up the original SN1a results, the evidence for the standard cosmological model is fairly strong now.
In reply to Coel Hellier: ok, i'll believe you;)
In reply to Coel Hellier: To look at it another way:

With the universal expansion above, objects 13 billion light years away are receding at the speed of light.

Is the fact that this 13 billion is close to the age of the universe purely a coincidence?

As far as I can see (leaving aside possible changes to the expansion rate) objects 13 billion light years away always have and always will be receding at the speed of light. I.e. it's got nothing to do with the age of universe. Or, has it?
In reply to Pero: HC= 42miles/s/3million light years:
Cox makes it simple again (21min+):
In reply to Pero: space and time are making love, or somesuch..
In reply to subalpine: Yes, I'm convinced now. Simple and wrong!

If Professor Cox repeated that calculation 7 billion years from now (assuming HC stays constant), he would get he same answer. But, that would no longer be the age of the universe.
In reply to Pero: There's much more complicated maths going on under the covers that he is skating over. It's not as simple as he makes out.

MASSIVE cake for all those candles
In reply to Pero: Coel will explain after he gives a full error analysis for the age of the universe..;)
In reply to Coel Hellier: as 'The most accurate determinations of the Hubble parameter H0 come from Type Ia supernovae'
http://en.wikipedia.org/wiki/Age_of_the_universe#Cosmological_parameters

if you took these out of the mix, how would that effect age of universe estimates and errors?

In reply to subalpine: I was quite happy with Brian Cox's calculation until I tried to understand the observable universe. What I've read on that states that any point in space that eventually gets 13 billion light years away will then be receding at the speed of light (and then faster and faster) and disappear from our observable universe for ever.

That shows that points in space are not receding from each other at a constant speed, but accelerating away from each other as they get further away.

And this seems to blow the simple inverse calculation for the age of the universe out the water.

> And this seems to blow the simple inverse calculation for the age of the universe out the water.

Nobody does a simple inverse calculation for the age, except as a very rough illustration. The usual estimates include the acceleration/deceleration of the universe.
In reply to Coel Hellier: Brian Cox did just that. And, for example:

http://csep10.phys.utk.edu/astr162/lect/cosmology/age.html

On this site, the author quite clearly states that t = d/v (which is only true for a constant velocity v). The calculation on this page is, on the face of it, nonsensical and it's pure coincidence that it approximates the age of the universe.

> if you took these out of the mix, how would that effect age of universe estimates and errors?

Age of the universe from recent WMAP CMB observations ( arXiv:1212.5225 ):

Including SNe 1a data: 13.77 +/- 0.06 Gyr.
Not including SNe data: 13.74 +/- 0.11 Gyr

> The calculation on this page is, on the face of it, nonsensical ...

No it isn't, it is perfectly sensible when teaching a subject to start with simplistic accounts of simple concepts, and then explain why they are too simple and introduce more sophisticated treatments.

> ... and it's pure coincidence that it approximates the age of the universe.

No it isn't a "pure coincidence", it says that the current value of H0 is comparable to the expansion rate that has obtained for much of the history of the universe. That is both true and tells us something about our universe.

In reply to Coel Hellier: Thanks very much for your help on this. To change the subject slightly, while I was looking at this I did notice that:

1 Parsec = 3.26 light years
1m = 3.28 feet

Coincidence, or what?

Coincidence.
>
> Age of the universe from recent WMAP CMB observations ( arXiv:1212.5225 ):
>
> Including SNe 1a data: 13.77 +/- 0.06 Gyr.
> Not including SNe data: 13.74 +/- 0.11 Gyr

assuming the models are correct?

For anyone still interested, I found this debate on the subject: