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zeromodz
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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
and the age of the universe being almost if not exactly the same
nicksauce said: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.
Well, the only difficulty with this analysis is that if you compared the age of our universe to [tex]1/H_0[/tex] much earlier than now or much later, you'd end up with a very very different result than the one we get.nicksauce said: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.
Chalnoth said:Well, the only difficulty with this analysis is that if you compared the age of our universe to [tex]1/H_0[/tex] 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.
hellfire said:The expression for the age of the universe in a general cosmological model is:
[tex]T = \frac{1}{H_0} \int_0^1 \frac{da}{\sqrt{ \Omega_{k, 0} + \displaystyle \frac{\Omega_{m,0} }{a} + \displaystyle \frac{\Omega_{r,0} }{a^2}+ \Omega_{\Lambda,0} a^2 \right)}}}[/tex]
Neglecting the radiation density, for the age to be equal to [itex]T = 1/H_0[/itex], it must hold that:
[tex]\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[/tex]
With [itex]\Omega_{k, 0} = 1 - \Omega_{m,0} - \Omega_{\Lambda,0}[/itex].
It would be nice to see graphically how the surface [tex]\mathcal{I}(\Omega_{m,0}, \Omega_{\Lambda,0})[/tex] behaves depending on different values of [itex]\Omega_{m,0}[/itex] and [itex]\Omega_{\Lambda,0}[/itex] (for example, between [0, 1]). Unfortunately I do not have the tools to do such graphics.
nicksauce said:Ah, I see what you mean now. Then yes, it is an interesting coincidence I suppose.
twofish-quant said:Or you can go anthropic and say that the universe needs about this much time for intelligent life to develop. One curious thing about this is that this would solve the Fermi paradox.
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.
Chalnoth said:If we take the flat case, that integral is within about 10% of 1 between around [tex]0.18 < \Omega_m < 0.38[/tex].
Given that the errors on those parameters is at the 2% level, this is probably a statistical fluke.Garth said:The present best accepted values of cosmological parameters
(using the table at WMAP Cosmological Parameters)
H0 = 70.4 km/sec/Mpsc
[itex]Omega_{\Lambda}[/itex] = 0.732
[itex]Omega_{matter}[/itex] = 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
Chalnoth said:Given that the errors on those parameters is at the 2% level, this is probably a statistical fluke.
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?Garth said: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
Garth said:DE densities are roughly equal in the present epoch, when they could be very disparate in value.
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.Chalnoth said: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?
Wallace said: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.
.The fact that the large number coincidence occurs only in the same epoch in which other coincidences among cosmic parameters occur could be considered a distinct coincidence problem suggesting an underlying physical connection.
Possible, but unlikely. The thing is, it's just not statistically significant enough to really tell us anything, at least not yet.Garth said: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
It might imply that you had unknowingly stumbled across a collection of wooden and steel rulers, we don't know.Wallace said:It's like saying if a piece of wood and a piece of metal are the same length it might imply a similarity in their internal chemistry.
We also don't know much about DM and DE, other than how they behave gravitationally, in particular we don't know how they relate to each other, but the A/TH coincidence AND the Cosmic Coincidence between [itex]\Omega_{DM}[/itex] and [itex]\Omega_{\Lambda}[/itex] might indicate that they are physically relevant parameters connected to each other.you can't find an underlying physical connection from these, because they are not physically relevant parameters, that is to say, they don't represent a physical theory, they are just some numbers.
A coincidence is an occurrence of two or more events that seem to be related or connected, but are not caused by each other. It is often perceived as a chance or random event.
Determining if something is just a coincidence can be difficult, as it often involves evaluating the probability and causation of the events. It is important to consider all possible explanations and gather evidence before coming to a conclusion.
Yes, many coincidences can be explained by science. For example, the "birthday paradox" is a coincidence that occurs when two people in a group share the same birthday, and it can be explained by probability and statistics.
It depends on the individual's interpretation and perspective. Some coincidences may hold personal significance or meaning, while others may not. It is important to consider the context and individual beliefs before determining the significance of a coincidence.
Coincidences occur all the time, as events are constantly happening around us. However, not all coincidences are noticeable or significant. It is a matter of perception and interpretation.