Why are the theoretical and measured sizes/ages of the universe so similar?

In summary, space expands evenly and objects are receding at a rate that is twice as fast when they are twice as far apart. This allows for a theoretical limit to the size of the observable universe, which is currently estimated to be around 150 billion light-years. The expansion rate of the universe is tied to the Hubble constant, which is approximately 14 billion years old and is a close match to the estimated age of the universe based on other measurements. However, it is worth noting that the Hubble constant is not constant over time. If we ignore factors such as gravity and the cosmological constant, the rate of expansion would be constant and the Hubble constant would be half its current value when the universe is twice its age.
  • #1
warpsmith
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Since space expands everywhere evenly, objects 2x as far apart recede twice as fast. It has been calculated that at a distance of 14 billion light-years (the Hubble distance), objects recede faster than light. This is OK since it is space itself is expanding.

This dictates a theoretical limit to the size of the observable universe (perhaps up to 150 B LY due to the expanding Hubble radius catching up with old light rays). This size of the observable universe is entirely due to the rate of expansion.

However, isn't it a HUGE coincidence that the rate of expansion matches almost exactly the best estimates for the size of the universe (also 14B LY) as determined by the ages of stars and other rate-independent measurements?

In other words (ignoring expansion acceleration and other wrinkles), won't the universe always seem to be about 14B years old, based solely on the Hubble constant? Couldn't the universe be MUCH older than 14B years?
 
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  • #2
warpsmith said:
In other words (ignoring expansion acceleration and other wrinkles), won't the universe always seem to be about 14B years old, based solely on the Hubble constant? Couldn't the universe be MUCH older than 14B years?
Hubble's "constant" is not constant over time.
 
  • #3
Yes, I'm aware of that :smile:

But it seems that the Hubble radius is 14B LY or so. This is due to the current rate of expansion. If for some reason the universe were 100B years old (not that I believe this, just making a point), it seems that at the same rate of expansion, we would still have a similar Hubble radius (since objects are expanded away FTL beyond that point).

I recognize that the observable universe is tied to but not equal to the Hubble radius, but these values seem independent of the age of the universe.
 
  • #4
warpsmith said:
Yes, I'm aware of that :smile:

But it seems that the Hubble radius is 14B LY or so. This is due to the current rate of expansion. If for some reason the universe were 100B years old (not that I believe this, just making a point), it seems that at the same rate of expansion, we would still have a similar Hubble radius (since objects are expanded away FTL beyond that point).
I recognize that the observable universe is tied to but not equal to the Hubble radius, but these values seem independent of the age of the universe.

If you ignore such things as gravity and the cosmological constant, then the rate of expansion would be constant. So when the universe is twice its current age, a galaxy will be twice as far away as it is now, but will have the same speed of recession. Hence the Hubble constant will be half what it is now.

Note that the limit of the observable universe is not due to objects traveling away faster than light, it is when we see back to the big bang (although the CMBR means that we can't actually see that far back). I've written more about this in http://www.chronon.org/Articles/cosmichorzns.html
 
  • #5
chronon,

very nice site!

I am still not understanding this. I am not trying to be obtuse or trying to propose some weird alternative theory - I just cannot get this straight in my head!

As I understand it, if you have dots one foot apart along an infinite elastic string, and the string is expanding at the same rate as the universe, then dots that are 14B LY apart are mathematically receding from each other at the speed of light. This is irrespective of how 'old' the string is or for how long it has been expanding. If the string had been expanding for 100B years, and you were to hop onto it and look down along it, then the dots 14B LY away would be receding FTL (you could still see a lot further, due to light leaving earlier in time, which makes the observable radius much further).

But if you didn't know how old the string was, wouldn't you just assume it was 14B years old based on the rate of expansion, when in fact it could be much older?

I'm not trying to argue static or regenerative models - I am just trying to grasp this one mathematical point.

Thanks for the help!
 
  • #6
warpsmith said:
But it seems that the Hubble radius is 14B LY or so. This is due to the current rate of expansion.
Actually, [tex]R(t) = \int_0^t \dot R(t) dt[/tex] rather than [tex]R(t) = \dot R(t) \cdot t[/tex] as is commonly assumed. This is a crucial distinction when [tex]\ddot R \neq 0[/tex].

warpsmith said:
If for some reason the universe were 100B years old (not that I believe this, just making a point), it seems that at the same rate of expansion, we would still have a similar Hubble radius (since objects are expanded away FTL beyond that point).

I recognize that the observable universe is tied to but not equal to the Hubble radius, but these values seem independent of the age of the universe.
If you assume the same rate of expansion, then when the universe is 100Gyr old the Hubble radius should span a distance several times greater than it is currently observed to.

warpsmith said:
This is irrespective of how 'old' the string is or for how long it has been expanding. If the string had been expanding for 100B years, and you were to hop onto it and look down along it, then the dots 14B LY away would be receding FTL (you could still see a lot further, due to light leaving earlier in time, which makes the observable radius much further).
If the two ends of the string had been moving apart at the speed of light for 100Gyr, then the dots 14Gly away would only be receding at 0.14 times the speed of light, would they not?
 
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  • #7
warpsmith said:
As I understand it, if you have dots one foot apart along an infinite elastic string, and the string is expanding at the same rate as the universe, then dots that are 14B LY apart are mathematically receding from each other at the speed of light. This is irrespective of how 'old' the string is or for how long it has been expanding. If the string had been expanding for 100B years, and you were to hop onto it and look down along it, then the dots 14B LY away would be receding FTL (you could still see a lot further, due to light leaving earlier in time, which makes the observable radius much further).
You seem to have a hidden assumption of some sort of acceleration in the expansion of the universe. If you assume this (i.e. a cosmological constant) then the universe would be older than 1/(Hubble constant). This was why the cosmological constant was taken seriously when 1/(Hubble constant) was thought to be about 2 billion years, that is younger than the Earth.

However, if you don't have any acceleration then Hubble's constant will decrease over time, since it is equal to speed/distance and the speed is constant while the distance is increasing. Hence your estimate of the age of the universe, which is based on 1/(Hubble constant) will increase.
 
  • #8
I feel unusually obtuse in the presence of two patient and kind tutors.

Aether said:
If the two ends of the string had been moving apart at the speed of light for 100Gyr, then the dots 14Gly away would only be receding at 0.14 times the speed of light, would they not?

No, I am assuming an infinite string with constant rate of expansion such that dots 14B LY apart are receding FTL (which models our universe).

chronon said:
However, if you don't have any acceleration then Hubble's constant will decrease over time, since it is equal to speed/distance and the speed is constant while the distance is increasing. Hence your estimate of the age of the universe, which is based on 1/(Hubble constant) will increase.

Almost got a flicker of comprehension from this. :smile: But I do not understand the part about the speed being constant, since from a fixed point the perceived recession rate increases with distance. Maybe I am off by one derivative of speed somehow...

Let me put forth my (a)ssumptions and (c)onclusions for you to demolish:

1a - assume no acceleration, gravity, or cosmological constant
2a - assume an infinite and eternally old string with dots at regular intervals
3a - assume the string between each dot expands at a fixed and constant rate
3c - this means that dots recede from all other dots at geometrically increasing rates as a function of distance
4a - assume the rate of expansion is equal to today's rate of expansion of the universe
4c - mathematically, dots 14B LY apart recede FTL
- (aside) this gives observable universes of up to 156B LY depending on whose math you believe in other posts :wink:
5a - you arrive at this string and attempt to determine the age of it
5c - you look in either direction and can see or calculate that the dot at 14B LY must be moving away at light speed
5c - you figure that dot must have been at your position 14B years ago
5c - you determine the string is 14B years old

I am completely aware that I am missing something painfully obvious. I just don't know what!
 
  • #9
You might like to read some of the papers by Lineweaver and Davis (several are referenced in the sticky here), or their recent article in Scientific American.

It may be that what you are interested in is beyond the scope of what addressed by Lineweaver and Davis, but at least it should rule out many of the common misunderstandings.
 
  • #10
Actually, it was Lineweaver's current article in SciAm (Misconceptions about the Big Bang) that sent me here! I thought I had it all straight until that article...

Thank you for the references. I will go off and do some reading.
 
  • #11
Yes, I believe this is a coincidence.

In the current model with H0 = 71 Km /s Mpc, [itex]\Omega_m = 0.27[/itex] and [itex]\Omega_{\Lambda} = 0.73[/itex] the "Hubble age" 1/H0 is nearly equal to the age of the universe. In this model 1/H0 = 13.7 Gyr. This implies that the comoving distance which enters the Hubble law to give a recession velocity c (this distance is called Hubble radius) is DcH = c / H0, equal to 13.7 GLyr. As an aside, the particle horizon is located at 46 GLyr (comoving distance).

This coincidence does not happen for every model. For example, an Einstein de-Sitter universe (flat space with [itex]\Omega_m = 1[/itex]), has an age of 9 Gyr at the time at which H0 = 71 Km /s Mpc. At this time t0, the Hubble age is obviously different to the age of the universe. Of course, at t0, the comoving distance at which the Hubble sphere is located is equal to 13.7 GLyr. The particle horizon is located at 27 GLyr.

This coincidence does also happen for other models, such as the Milne universe, with H0 = 71 Km /s Mpc, [itex]\Omega_m = \Omega_{\Lambda} = 0[/itex], but there are lots of universes for which this coincidence does not occur. I cannot tell you whether there is a deeper reason behind this.
 
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  • #12
I have been thinking about this and I came to the conclusion that the fact that this coincidence arises in the Milne universe (linearly expanding universe) is natural (actually it is not a coincidence in that model). In that model t = 1/H, for every t, since [itex]\dot a = k[/itex] (the first time derivative of the scale factor is a constant; note that [itex]H = \dot a / a[/itex]). I wonder now whether there is an explanation for the the similarity between the Milne universe and the concordance model today at H0 = 71 Km/s Mpc.
 
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  • #13
Some think the Milne universe i.e. here ought to be the concordance model!
 
  • #14
I object. Nucleosynthesis does not work in the Milne model. It could, however, work in other reference frames.. like BD.
 
  • #15
Chronos said:
I object. Nucleosynthesis does not work in the Milne model. It could, however, work in other reference frames.. like BD.
Others would disagree, for example Kolb Nucleosynthesis in a Simmering Universe and the Indian team (Daksh Lohiya, Annu Batra, Shobhit Mahajan, Amitabha Mukherjee, Department of Physics & Astrophysics, University of Delhi) A coasting cosmology

Of course the GR Milne model is empty and so has no nucleosynthesis, however the freely coasting model is modified GR theory which is based on a Milne universe (R ~ t, k = -1)

Note the SCC Jordan conformal frame model is (R ~ t, k = +1) but the k = +1 and k = -1 models converge in the early universe, and so the freely coasting nucleosynthesis applies to SCC as well.

Garth
 
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1. Why is the measured age of the universe so close to the theoretical age?

There are several factors that contribute to the close similarity between the theoretical and measured ages of the universe. One of the main factors is the accuracy of our current scientific models and theories, which have been continuously refined and tested over time. Another factor is the precision of the instruments and technology used to measure the age of the universe, which has greatly improved in recent years. Additionally, the laws of physics that govern the expansion and evolution of the universe are well-understood and can be used to make accurate predictions of its age.

2. How do scientists measure the age of the universe?

Scientists use a variety of methods to measure the age of the universe, including the cosmic microwave background radiation, the distance and speed of galaxies, and the age of the oldest stars. These methods are all based on our current understanding of the expansion and evolution of the universe, and when combined, provide a range of ages that are consistent with each other.

3. Are there any discrepancies between the theoretical and measured sizes of the universe?

While there may be some small discrepancies between the theoretical and measured sizes of the universe, they are generally very close. These discrepancies can be attributed to the limitations of our current technology and models, as well as the challenges of accurately measuring something as vast and complex as the universe.

4. How does the expansion of the universe affect its measured size and age?

The expansion of the universe does not significantly impact its measured size, as the rate of expansion is relatively constant. However, it does have an impact on the age of the universe. The faster the expansion, the younger the universe appears to be, and vice versa. This is taken into account when measuring the age of the universe.

5. Could the measured age of the universe change in the future?

While it is always possible that new discoveries or advancements in technology could lead to a change in the measured age of the universe, the current methods and theories used to determine its age are constantly being refined and tested. Therefore, any changes in the measured age of the universe would likely be small and still consistent with the current theoretical age.

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