# Is this just a coincedence?

1. Jan 2, 2010

### zeromodz

Is it just a coincidence that Hubble's Sphere which is c/H

and the age of the universe being almost if not exactly the same

2. Jan 3, 2010

3. Jan 3, 2010

### nicksauce

I don't see it as a coincidence. If you admit only c and Ho as the only constants with dimensions in your model, then you would expect them to give the characteristic length scale c/Ho and the characteristic time scale 1/Ho. In other words, the age of the universe must be of order 1/Ho, because there are no other numbers you can play around with to give a time.

4. Jan 3, 2010

### Garth

The Age of the universe A is not necessarily equal to Hubble Time TH = H-1.

In GR without DE
$$T_H \geqslant A \geqslant \frac{2}{3} T_H$$
depending on a cosmological density of $0 \geqslant \Omega \geqslant 1$.

The actual density was generally thought (pre 1998) not to be greater than the critical density because i) such density was not observed and ii) that would introduce an Age Problem to the model.

However, after 1998, in the LCDM model with DE: A can be $( \frac{2}{3} \rightarrow \infty)T_H$ depending on the amount of density and DE.

Why then should there be just enough DE and total density so that A is so close to $T_H$ that it is exactly equal to it to within observational errors?

You will find a discussion on this topic on the thread I linked to above.

Garth

Last edited: Jan 3, 2010
5. Jan 3, 2010

### Chalnoth

Well, the only difficulty with this analysis is that if you compared the age of our universe to $$1/H_0$$ much earlier than now or much later, you'd end up with a very very different result than the one we get.

I'm sure I could calculate this more explicitly, but my suspicion is that this is another feature of the cosmological coincidence problem: that the matter and dark energy density are both within an order of magnitude of one another right now.

6. Jan 3, 2010

### Garth

Well as hellfire said in this post:
There you have the relationship between the matter and DE densities, but why should the integral pretty well equal unity?

I cannot help but see it as more than just a coincidence.

Garth

7. Jan 3, 2010

### nicksauce

Ah, I see what you mean now. Then yes, it is an interesting coincidence I suppose.

8. Jan 3, 2010

### twofish-quant

One thing that would be interested is to do a calculation in which you estimate the earliest point in the universe in which intelligent life could develop and then the latest point, and the compare that with Hubble times.

9. Jan 3, 2010

### Garth

If you look at the integral:
$$\mathcal{I}(\Omega_{m,0}, \Omega_{\Lambda,0}) = \int_0^1 \frac{da}{\sqrt{ \Omega_{k, 0} + \displaystyle \frac{\Omega_{m,0} }{a} + \Omega_{\Lambda,0} a^2 \right)}}} = 1$$

With $\Omega_{k, 0} = 1 - \Omega_{m,0} - \Omega_{\Lambda,0}$.

You see both Hubble Time and the Age of the universe are nowhere to be seen.

In order to get the 'coincidence' you need the correct balance of Matter, Dark Matter and Dark Energy.

Then, with that relative abundance ratio, you would get the coincidence at all ages of the universe.

Garth

10. Jan 4, 2010

### Chalnoth

If we take the flat case, that integral is within about 10% of 1 between around $$0.18 < \Omega_m < 0.38$$.

11. Jan 4, 2010

### Garth

The present best accepted values of cosmological parameters
(using the table at WMAP Cosmological Parameters)
H0 = 70.4 km/sec/Mpsc
$Omega_{\Lambda}$ = 0.732
$Omega_{matter}$ = 0.268

Feeding these values into Ned Wright's Cosmology Calculator:
The age of the universe is = 13.81 Gyrs.
But with h100 = 0.704,
Hubble Time = 13.89 Gyrs.

So the integral is equal to A/TH = 0.994, i.e. to within 0.6% of unity.

Garth

12. Jan 4, 2010

### Chalnoth

Given that the errors on those parameters is at the 2% level, this is probably a statistical fluke.

13. Jan 5, 2010

### Garth

However, note in precision cosmology the values of H and A are given to 3 decimal places, so rounding to 2 places, A and TH are equal to within observational errors.

Garth

Last edited: Jan 5, 2010
14. Jan 5, 2010

### Wallace

It doesn't matter how close to unity this integral is, the whole co-incidence is a red herring. Since the age of the Universe is a derived quantity, not a model parameter, it doesn't matter what value it has (beyond any 'age problems' which don't seem overwhelming at this point, and not relevant to any co-incidence in any case).

Everytime this comes up, people want to try and suggest that this is somehow a problem for LCDM or that is points to some alternate model, but you can't make model selection decisions based on derived quantities after you have considered the data. If some other model exists that would say enforce this co-incidence to be true at all times (and hence not be a co-incidence) then the only way to test that model is against the original data, not against the derived age from the fit of the LCDM model to the data.

To put it another way, an infinite number of incompatible models could give you the same age, so looking at the age alone tells you nothing.

15. Jan 5, 2010

### Garth

So A/TH ~ 1 is just a coincidence in the LCDM model.

As the drived age A is dependent on $\Omega_m$ and $\Omega_{\Lambda}$, it is obviously related by the integral in post 9 to the Cosmic Coincidence Problem in that model which is the DM (and baryonic matter) and DE densities are roughly equal in the present epoch, when they could be very disparate in value.

Garth

Last edited: Jan 5, 2010
16. Jan 5, 2010

### Chalnoth

But as I said, if those parameters are only measured to within 2%, any measurement that they are closer than that is likely just a fluke. Did you try looking at other combinations of data, for instance?

17. Jan 5, 2010

### Wallace

They could be, but they don't appear to be so. Just as I could have made this post at any moment, but against all odds happened to make it at precisely 11:36 am (CET) on the 5th of January 2010!

Less facetiously, there really isn't a big deal about this co-incidence in energy densities. If you start from the assumption that you are in a Lambda /= 0 universe, and can actually observe this cosmologically, then it is not so surprising to see this confluence. If we existed to early we'd just see matter domination and if we exist too late we'd see nothing outside the local group.

There are a lot of more pressing problems in cosmology that one could get your knickers in a knot about than a few curious numerological co-incidences.

18. Jan 5, 2010

### Garth

I agree that the fact that A and TH are within 0.6% of each other is a fluke and by choosing slighty different values (within the error bars) for the densities the answer would come out less close, but the fact that they are equal within observational error (i.e. closer than 2%) might be telling us something about the relationship between matter, DE and DM.

Garth

Last edited: Jan 5, 2010
19. Jan 5, 2010

### Garth

Well, I'm not getting my knickers in an twist, it might just be a coincidence, I was simply responding to the OP question!

However, others do think about the Cosmic Coincidence Problem such as here and as Funkhouser says:
.

In may prove interesting not to dismiss such coincidences as 'just coincidences' in order to explore a possible "underlying physical connection".

Garth

Last edited: Jan 5, 2010
20. Jan 5, 2010

### Chalnoth

Possible, but unlikely. The thing is, it's just not statistically significant enough to really tell us anything, at least not yet.

If we started to measure these parameters to within, say, 0.05% or so, and the age was still, within the error bars, equal to the inverse of the Hubble constant, then we might have something that really needs explaining. But within 2%? That's not really special.