Speed of Universe's Expansion Measured Better Than Ever

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Speed of Universe's Expansion Measured Better Than Ever

Postby weakmagneto on October 8th, 2012, 8:13 pm 

I just came across this article published Oct 4/12 in Scientific American and thought I should share it.

The newest measurements, courtesy of NASA's Spitzer Space Telescope, come from infrared observations of distant variable stars.

The most precise measurement ever made of the speed of the universe's expansion is in, thanks to NASA's Spitzer Space Telescope, and it's a doozy. Space itself is pulling apart at the seams, expanding at a rate of 74.3 plus or minus 2.1 kilometers (46.2 plus or minus 1.3 miles) per second per megaparsec (a megaparsec is roughly 3 million light-years).

If those numbers are a little too much to contemplate, rest assured that's really, really fast. And it's getting faster all the time.

American astronomer Edwin P. Hubble first discovered that our universe isn't static in the 1920s. In fact, Hubble found, space has been expanding since it began with the Big Bang 13.7 billion years ago. Then, in the 1990s, astronomers shocked the world again with the revelation that this expansion is speeding up (this discovery won its finders the 2011 Nobel Prize in physics).

Ever since Hubble's initial discovery, scientists have been trying to refine their measurement of the universe's expansion rate, called the Hubble Constant. It's a hard measurement to make.

The new value reduces the uncertainty in the Hubble Constant to just 3 percent, and improves the precision of the measurement by a factor of three compared to a previous estimate from the Hubble Space Telescope.

"Just over a decade ago, using the words 'precision' and 'cosmology' in the same sentence was not possible, and the size and age of the universe was not known to better than a factor of two," Wendy Freedman of the Observatories of the Carnegie Institution for Science in Pasadena, Calif., said in a statement. "Now we are talking about accuracies of a few percent. It is quite extraordinary." [7 Surprising Facts About the Universe]

The new measurement doesn't just tell scientists how fast the universe is expanding, but helps shed light on the mystery of why this expansion is accelerating. Dark energy is the name given to whatever is causing the universe's expansion to speed up. Yet scientists have little idea what it is.

By combining the new value of the Hubble Constant with observations of the universe by NASA's Wilkinson Microwave Anisotropy Probe (WMAP), the scientists were able to make an independent calculation of the strength of dark energy, which is battling against gravity to pull the universe outward.

"This is a huge puzzle," Freedman said. "It's exciting that we were able to use Spitzer to tackle fundamental problems in cosmology: the precise rate at which the universe is expanding at the current time, as well as measuring the amount of dark energy in the universe from another angle."


http://www.scientificamerican.com/artic ... -expansion
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 9th, 2012, 12:22 am 

It will be interesting to see if this causes change to the other cosmological parameters. If they do not change, the universe must be younger, only some 13.0 billion years, a good 500 million years younger than the present best fit.

But I suspect that if this Ho stands up to scrutiny, the other parameters will follow suite and the age will remain largely unchanged.

Edit: SciAm's sensational "Space itself is pulling apart at the seams, expanding at a rate of 74.3..." is a bit overboard, conjuring up images of a 'big-rip', which is obviously not the case. It is still compatible with standard lambda-expansion, accelerating at a rather sedate rate.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby Marshall on October 9th, 2012, 2:11 am 

Hi Jorrie glad to see you! Hi Mageto, that's a good find. I didn't know of it although the technical paper I now see came out in August:
http://arxiv.org/abs/1208.3281
Carnegie Hubble Program: A Mid-Infrared Calibration of the Hubble Constant

Wendy L. Freedman, Barry F. Madore, Victoria Scowcroft, Chris Burns, Andy Monson, S. Eric Persson, Mark Seibert, Jane Rigby
(Submitted on 16 Aug 2012)
Using a mid-infrared calibration of the Cepheid distance scale based on recent observations at 3.6 um with the Spitzer Space Telescope, we have obtained a new, high-accuracy calibration of the Hubble constant. We have established the mid-IR zero point of the Leavitt Law (the Cepheid Period-Luminosity relation) using time-averaged 3.6 um data for ten high-metallicity, Milky Way Cepheids having independently-measured trigonometric parallaxes. We have adopted the slope of the PL relation using time-averaged 3.6 um data for 80 long-period Large Magellanic Cloud (LMC) Cepheids falling in the period range 0.8 < log(P) < 1.8. We find a new reddening-corrected distance to the LMC of 18.477 +/- 0.033 (systematic) mag. We re-examine the systematic uncertainties in H0, also taking into account new data over the past decade. In combination with the new Spitzer calibration, the systematic uncertainty in H0 over that obtained by the Hubble Space Telescope (HST) Key Project has decreased by over a factor of three. Applying the Spitzer calibration to the Key Project sample, we find a value of H0 = 74.3 with a systematic uncertainty of +/-2.1 (systematic) km/s/Mpc, corresponding to a 2.8% systematic uncertainty in the Hubble constant. This result, in combination with WMAP7 measurements of the cosmic microwave background anisotropies and assuming a flat universe, yields a value of the equation of state for dark energy, w0 = -1.09 +/- 0.10. Alternatively, relaxing the constraints on flatness and the numbers of relativistic species, and combining our results with those of WMAP7, Type Ia supernovae and baryon acoustic oscillations yields w0 = -1.08 +/- 0.10 and a value of N_eff = 4.13 +/- 0.67, mildly consistent with the existence of a fourth neutrino species.
27 pages, 8 figures, to be published in ApJ.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby yadayada on October 9th, 2012, 2:33 am 

BurtJordaan wrote:It will be interesting to see if this causes change to the other cosmological parameters. If they do not change, the universe must be younger, only some 13.0 billion years, a good 500 million years younger than the present best fit.

But I suspect that if this Ho stands up to scrutiny, the other parameters will follow suite and the age will remain largely unchanged.

I was thinking along similar lines. The Hubble constant cannot creep up without causing discomfort, because then the age of the universe becomes lower. Adjusting the other parameters is the usual solution, but that sort of post hoc subjectivity of parameters upsets any historian or philosopher of science.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 9th, 2012, 3:06 am 

yadayada wrote:
BurtJordaan wrote:It will be interesting to see if this causes change to the other cosmological parameters. If they do not change, the universe must be younger, only some 13.0 billion years, a good 500 million years younger than the present best fit.

But I suspect that if this Ho stands up to scrutiny, the other parameters will follow suite and the age will remain largely unchanged.

I was thinking along similar lines. The Hubble constant cannot creep up without causing discomfort, because then the age of the universe becomes lower. Adjusting the other parameters is the usual solution, but that sort of post hoc subjectivity of parameters upsets any historian or philosopher of science.

I checked the Freedman 2102 paper that Marshall referenced. The values fitting the most observations (bottom row of table 2, page 20) gives Omega_m = 0.278 nominal, meaning Omega_Lambda = 0.722. According to my modeling, this correlates with the following values:

T_Hub(now) = 13.2 Gy,
T_Hub(inf) = 15.5 Gy and
T_now = 12.96 Gy.
T_rec = 367,000 years.

So it seems that the 'age of expansion' did indeed come down. It does not make a big difference, e.g. the time of the emission of that latest 'most distant' galaxy at z=9.6, comes down from 500 million to 480 million years after T0. For most practical purposes, this is neither here nor there...

Jorrie
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby yadayada on October 9th, 2012, 4:13 am 

Thank you so much for checking that for me. One thing I noticed is that the study is based on the observation of Cepheid type variable stars. This makes it relatively short ranged, only up to the limits of luminosity and resolution of stars in nearby galaxies. Other studies of much rarer supernova explosions extend the range somewhat. The difference is that the nearer, and therefore more recent universe is expanding at a higher rate than the earlier universe. The early universe must have been considerably lower still.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 9th, 2012, 4:59 am 

yadayada wrote:One thing I noticed is that the study is based on the observation of Cepheid type variable stars. This makes it relatively short ranged, only up to the limits of luminosity and resolution of stars in nearby galaxies. Other studies of much rarer supernova explosions extend the range somewhat. ...

The Cepheid 'rung' was the least accurate in the distance ladder for some time now, so it was important to try and improve on it. Broadly, there are three very important rungs: parallax inside the MW overlaps with Cepheids inside the MW and nearby galaxies and clusters like Virgo. SNe Ia then overlaps with the Cepheids in the clusters, giving us a distance-brightness calibration up to SNe Ia at z=1.4. Since we also have the redshift of clusters like Coma, this determines Ho, which we can then use to find the distances out to as far as we can measure the redshifts of galaxies or quasars, e.g. around z=10.

yadayada wrote:The difference is that the nearer, and therefore more recent universe is expanding at a higher rate than the earlier universe. The early universe must have been considerably lower still.

The data is giving us the magnitude of this difference and we use that in our models. If our model is correct, then it is just a matter of constraining all the variables to better and better accuracy.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby Marshall on October 11th, 2012, 12:28 pm 

yadayada wrote:...The difference is that the nearer, and therefore more recent universe is expanding at a higher rate than the earlier universe. The early universe must have been considerably lower still.


Hi Yada,
could you please provide some clarification and professional corroboration?

It's hard for me to make sense of what you say here. What do you means by "rate"?
The natural thing to mean by that is the Hubble expansion rate H(t) which does change over time.

But if you know anything about cosmology I'm sure you realize that it would be totally crackpot to imagine that the Hubble expansion rate has been increasing :^D.
So what "rate" do you mean, exactly, that is higher now than in the past?
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby Marshall on October 11th, 2012, 1:02 pm 

BurtJordaan wrote:I checked the Freedman 2012 paper that Marshall referenced. The values fitting the most observations (bottom row of table 2, page 20) gives Omega_m = 0.278 nominal, meaning Omega_Lambda = 0.722. According to my modeling, this correlates with the following values:

T_Hub(now) = 13.2 Gy,
T_Hub(inf) = 15.5 Gy and
T_now = 12.96 Gy.
T_rec = 367,000 years.

So it seems that the 'age of expansion' did indeed come down...


Table 2 is exciting! Wendy Freedman and Barry Madore are central people. The last row of that table carries a lot of weight for me. We have to consider the uncertainty ranges too!
There even seems to be a substantial chance for positive curvature and finite spatial volume. Omega_k negative means Omega_total > 1.

H0+WMAP7+BAO+SNLS (supernova legacy survey)
· ·
Omegak = −0.007 ± 0.007
Omegatotal = 1.007 ± 0.007

Omegam = 0.278 ± 0.018
w0 = −1.08 ± 0.10
Neff = 4.13 ± 0.67

I am not sure how to estimate OmegaLambda except by ADDING the uncertainties, which gives
Omegatotal- Omegam = (1.007 ± 0.007) - ( 0.278 ± 0.018) = 0.729 ± 0.025

So I put this into google:
1/(74.3 km/s per Mpc) /sqrt(.729)
and get out 15.4 billion years for the longterm Hubbletime Yinf
and of course agree with your figure 13.2 billion years for the current Ynow.
I'll go put 13.2 and 15.4 into the A25 calculator and see what expansion age I get.
I get age = 13.2 Gy
Marshall
 


Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 11th, 2012, 1:04 pm 

Marshall wrote:
yadayada wrote:...The difference is that the nearer, and therefore more recent universe is expanding at a higher rate than the earlier universe. The early universe must have been considerably lower still.


Hi Yada,
could you please provide some clarification and professional corroboration?

It's hard for me to make sense of what you say here. What do you means by "rate"?
The natural thing to mean by that is the Hubble expansion rate H(t) which does change over time.

But if you know anything about cosmology I'm sure you realize that it would be totally crackpot to imagine that the Hubble expansion rate has been increasing :^D.
So what "rate" do you mean, exactly, that is higher now than in the past?


Marshall, I'm afraid I don't understand your question ;)
The Hubble constant is a recession rate, not an expansion rate. Yada's statement on expansion rate seems correct to me. ??
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby Marshall on October 11th, 2012, 1:44 pm 

How does one define "expansion rate" mathematically?

I assumed it was something like the km/s at a particular fixed distance like Mpc.

In which case it seems equivalent to the Hubble parameter. So if the H declines so does the expansion rate.
this is really curious.
I've always logically equated expansion of distance with recession. Very interested to hear how the two are mathematically defined so that they are distinct!
=================

BTW Jorrie that 2012 paper of Wendy Freedman et al sounds PRELIMINARY to me. They talk of their new Spitzer project as if they are at the beginning and will have more to say. that's just my take on it and I would be interested in how you read the situation.

Right now I do not expect the new Freedman et al figures to be immediately accepted---the dust still has to settle quite a bit. Just my hunch.

For one thing there are the ISOTOPE dating estimates of the oldest stars. These estimates have a large uncertainty and different methods of dating can say different things. But you get some estimates of 13.2 Gy (plus or minus something) for stars in globular clusters. Particularly that "Thorium/Europium" dating method. I don't know how reliable that is. Am I wrong? You may know a good deal more about this than I do.

Now the first stars may have been very massive and had very short lifetimes on the order of a few million years---on the order of 0.001 Gy, And we are still trying to determine when reionization began---that is when the first stars formed. So there is a good deal of leeway.

But it still seems to me (as amateur watcher from sidelines) that the new Freedman et al numbers give an age which is bumping against the age of oldest stars.
Marshall
 


Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 11th, 2012, 2:57 pm 

Marshall wrote:How does one define "expansion rate" mathematically?

I assumed it was something like the km/s at a particular fixed distance like Mpc.

In which case it seems equivalent to the Hubble parameter. So if the H declines so does the expansion rate.
this is really curious.
I've always logically equated expansion of distance with recession. Very interested to hear how the two are mathematically defined so that they are distinct!

As I have it, expansion rate is simply a-dot (i.e. da/dt), while recession rate H = a-dot/a. Presently a-dot is increasing (accelerated expansion), while H is decreasing. Later on, a will increase as fast a-dot (compound interest), hence a constant H.

I agree with you that the jury is probably still out on the 2012 Freedman results.

We had a severe thunderstorm, causing a power outage, so I will probably have to sign out before depleting the battery. Fortunately 3G cell towers are operating...
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby Marshall on October 11th, 2012, 3:58 pm 

BurtJordaan wrote:...
I agree with you that the jury is probably still out on the 2012 Freedman results.

We had a severe thunderstorm, causing a power outage, so I will probably have to sign out before depleting the battery. Fortunately 3G cell towers are operating...


Out of solidarity (and consideration for your battery) I will stop posting for a while. Let us know when power is back on!

I see what you mean.

H(t) = a'/a = - S'/S
so we can solve for a' any of a variety of ways and talk about it. Now I shall be QUIET until the power goes back on :^D
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby yadayada on October 11th, 2012, 8:59 pm 

I discovered the following (to me) interesting overview of the observational evidence for the age of the universe.
http://astro.berkeley.edu/~dperley/univage/univage.html
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 12th, 2012, 12:22 am 

Marshall wrote:
I see what you mean.

H(t) = a'/a = - S'/S
so we can solve for a' any of a variety of ways and talk about it. Now I shall be QUIET until the power goes back on :^D

Took most of our night to repair distribution system, but we are recharged. :-)

One can say a' is the proper rate of expansion and H(t) is the fractional rate of expansion (%-like), but I prefer to stick to H as the recession rate per unit distance. They both have the same units (time-1), so it can sometimes be confusing.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby Marshall on October 12th, 2012, 1:17 am 

Glad power has been restored!
About the technical definitions. Expansion sounds like recession enough that newcomers may not at first get that very different things are meant.
For now my guess is that the only way to be sure of being understood is to use some redundancy. Use enough words in each post so it's clear. So I favor "fractional rate of expansion". Never introduce "km/s" into that context if I can help it because newcomers automatically visualize it as speed of something moving thru space.

But we'll see. Discussion boards are a kind of testing laboratory of how to communicate things like this clearly and your idea may succeed.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 12th, 2012, 1:30 am 

yadayada wrote:I discovered the following (to me) interesting overview of the observational evidence for the age of the universe.
http://astro.berkeley.edu/~dperley/univage/univage.html

Nice link, Yada.

It looks like the margins (table 4) are wide enough so that any cosmic age above ~12 Gyr can be accommodated, so the Freedman 2012 data giving ~13 Gyr is no problem.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 12th, 2012, 2:52 am 

Marshall wrote:Glad power has been restored!..
For now my guess is that the only way to be sure of being understood is to use some redundancy. Use enough words in each post so it's clear. So I favor "fractional rate of expansion".

Yes, maybe the compact, yet definitive terms "proper expansion rate" for a' and "fractional expansion rate" for H is the way to go.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby Marshall on October 12th, 2012, 6:49 am 

I'd happily go along with that if you decide you like that usage. It's clear, descriptive and has a kind of conventional sound.

I also liked the Dan Perley page that Yada linked to. He got his PhD from Berkeley in 2011 and is now at Caltech. I think he created that webpage on the "Age of Universe" back in 2004, and gives his address as 601 Campbell Hall (where the astrophysics grad students used to hang out). He did a nice job with that webpage. It's educational especially the animation of the H-R diagram and the other graphics.
I see that he cites Ned Wright's FAQ about "Age of Universe", which is also very good, and has been updated since then.

Ned Wright does something that Perley doesn't: He takes the equivalent of Perley's Table 4 and does a *weighted average* of the different estimates. If I understand right, I think that takes into account their different-size range of uncertainties and comes up not only with an average age but also a combined uncertainty. when he puts all the estimates together he comes up with something around 13 Gy plus or minus something like 1 Gy. He cites some of the same sources as Perley, and a few others. Good explanation of the different dating techniques used.
http://www.astro.ucla.edu/~wright/age.html
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 12th, 2012, 12:03 pm 

Marshall wrote: ...
Ned Wright does something that Perley doesn't: He takes the equivalent of Perley's Table 4 and does a *weighted average* of the different estimates. If I understand right, I think that takes into account their different-size range of uncertainties and comes up not only with an average age but also a combined uncertainty. when he puts all the estimates together he comes up with something around 13 Gy plus or minus something like 1 Gy. ...

I also think Ned Wright's pages are excellent stuff for serious students of any level, but perhaps not quite for fairly raw beginners. My experience is that such readers do not read equations, so it's wasted effort on both sides, reader as well as writer.

BTW, it's interesting that Ned's weighted median age of 12.94 Gyr is almost exactly what our model says for the Freedman 2012 'flat' median data, 12.96 Gyr (that I used above):

[quote=Jorrie]
"Omega_m = 0.278 nominal, meaning Omega_Lambda = 0.722.
According to my modeling, this correlates with the following values:
T_Hub(now) = 13.2 Gy,
T_Hub(inf) = 15.5 Gy and
T_now = 12.96 Gy.
"
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 12th, 2012, 12:30 pm 

Marshall wrote:...
I am not sure how to estimate OmegaLambda except by ADDING the uncertainties, which gives
Omegatotal- Omegam = (1.007 ± 0.007) - ( 0.278 ± 0.018) = 0.729 ± 0.025

So I put this into google:
1/(74.3 km/s per Mpc) /sqrt(.729)
and get out 15.4 billion years for the longterm Hubbletime Yinf
and of course agree with your figure 13.2 billion years for the current Ynow.
I'll go put 13.2 and 15.4 into the A25 calculator and see what expansion age I get.
I get age = 13.2 Gy


Sorry, with the power outage, I missed this one of yours.

The age 13.2 is obviously too high for a Ynow = 13.2 Gyr. I fine tuned the values of Y_now and Y_inf with more decimals to get closer to the Freedman values for Ho and Omega_m and got a more realistic value, I think.

PS: if you have read this pre my last edit, I also messed up with those values.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby Marshall on October 12th, 2012, 11:16 pm 

I must not have seen pre edit. I haven't seen anything messed. But my eyesight isn't perfect and I miss things especially late in the evening. I'm glad Magneto nudged our attention towards this Wendy Freedman et al work.

http://arxiv.org/pdf/1208.3281v1.pdf especially Table 2 on page 20.

I decided that even though their work is preliminary and not yet accepted by the community, so that it is premature for me to take it seriously, that I WANT to take it seriously. And for the time being I want to ignore the errorbars of uncertainty and just look at the central values of the parameters Freedman et al. AFAIK, looking at their Table 2, here they are:
Ho = 74.3
Omega_matter = 0.278
Omega_Lambda = 0.729

That is what leads to an age = 12.985 Gy.

I don't know why, can't justify it. I just feel happy. For one thing Magneto called attention to this and Wendy Freedman leads the Spitzer team, and it uses the Henrietta Leavitt law of Cepheids. It's good for the blood circulation in our cortexes to have women involved in cosmology. Improves the oxygen supply to the brain. Maybe you feel the same way. So let's see how the universe looks with those parameters. And let's not necessarily round off to 3 decimal places right away, you never know.

Doing the usual thing, putting 1/(74.3 km/s per Mpc) into google I get Y_now = 13.16 Gy
and putting 13.16 into the A25 I find that I have to set Y_infinity = 15.49 Gy

Of course this Freedman et al universe (with central values) is spatially round not flat and the A25 calculator, my favorite :^D assumes flat, but let's ignore that and put in the two hubbletimes. Just for the heck of it.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby Marshall on October 13th, 2012, 12:37 am 

When I put those two hubbletimes in: 13.16 and 15.49, I get a present age of 12.952 Gy.
That is fairly close to the 12.985 that I got from the original Freedman et al numbers.

Should I have recalculated the crossover? I just kept that 3350 unchanged. For now I won't worry about that.

But if we are increasing H to 74.3 that means increasing rho_crit and also we are increasing Omega_matter so that means we are throwing in some extra dark matter and radiation density as a fraction of matter is going to decline, so the number 3350 ought to increase some.

Just playing around, I took crossover to 3500, set the hubbletimes to 13.17 Gy and 15.47 Gy and A25 said that the present age was 13.000.

It is never going to match Freedman et al precisely because it never gets Omega_total slightly bigger than one the way they have. So the Omega_matter and Omega_Lambda are always going to look just a tiny bit skimpy. But it does a good imitation of Freedman et al!

13.17 gives you something that rounds up to their 74.3. I think it comes to 74.26. Close enough.
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 13th, 2012, 12:51 am 

Marshall wrote:Doing the usual thing, putting 1/(74.3 km/s per Mpc) into google I get Y_now = 13.16 Gy
and putting 13.16 into the A25 I find that I have to set Y_infinity = 15.49 Gy

Of course this Freedman et al universe (with central values) is spatially round not flat and the A25 calculator, my favorite :^D assumes flat, but let's ignore that and put in the two hubbletimes. Just for the heck of it.


It's been quite some time now that there is a slight statistical bias towards a closed geometry. Omegak = -0.007 translates to a cosmic radius near 40 Hubble radii (I think?), so no good reason to consider anything but flat, I guess. And since nothing outside the Hubble radius should ever influence us again, ...
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby Marshall on October 13th, 2012, 1:04 am 

I think 40 is about right. The square root of .007 is 1/12
So the radius of curvature of a hypersphere with the indicated curvature is 12 times the hubbleradius.
So the circumference of the hypersphere is 6.28 times 12 times hubbleradius.

So the farthest away from home you can ever get is about 40 hubble radii. Is that how you were figuring?
Twelve times 3.14 is about 40?
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Re: Speed of Universe's Expansion Measured Better Than Ever

Postby BurtJordaan on October 13th, 2012, 1:26 am 

Marshall wrote:I think 40 is about right. The square root of .007 is 1/12
So the radius of curvature of a hypersphere with the indicated curvature is 12 times the hubbleradius.
So the circumference of the hypersphere is 6.28 times 12 times hubbleradius.

So the farthest away from home you can ever get is about 40 hubble radii. Is that how you were figuring?
Twelve times 3.14 is about 40?


Yup, that's it. :-)



We can obviously never even reach 1 Hubble radius from here...

-J
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