
#1
Nov912, 04:40 PM

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PF Gold
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I just posted about the new parameters here:
http://physicsforums.com/showthread....80#post4152380 Basically the new numbers look rather close to what Jorrie already put as the default in his calculator. z_{EQ} looks familiar. Hubble rate 70 looks familiar Here's the A25 calculator: http://www.einsteinstheoryofrelat...oLean_A25.html Sean Carroll has a blog post about the new SPT report. http://blogs.discovermagazine.com/co...bconstraints/ 



#2
Nov1012, 08:40 PM

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A curious thing about the SPT report is that it implies with 95% confidence the U is spatially finite. (Not just the observable portion, the whole thing.) They gave a errorbar or confidence interval for the overall largescale curvature which was all to the positive. Precisely flat, zero curvature, seems to be RULED OUT if you take seriously the SPT report. Here is their confidence interval for Omega.
1.0019 < Omega < 1.0099 If you accept their Hubble radius of 14.0 billion LY (which is very close to what other recent studies have found) then we are talking about space, in the standard LCDM model, being a hollow 3sphere with radiusofcurvature no larger than 14/sqrt(0.0019) = 320 billion LY. In fact this brackets the radius of curvature R: 140 Gly < R < 320 Gly So we can imagine CIRCUMNAVIGATING the universe, if we could somehow halt its expansion so that its circumference wouldn't be growing while we were making the circuit. 6.28*140 = 880 6.28*320 = 2010 So the South Pole Telescope folks are telling me that I stop the expansion and shoot a laser flash off in some direction then eventually it will come back to me from the other direction, having circumnavigated space. And it will take AT LEAST 880 billion years to come around back and NO MORE than 2010 billion years. See equation 21 on page 14, of http://arxiv.org/pdf/1210.7231v1.pdf 



#3
Nov1012, 09:52 PM

PF Gold
P: 11,055

Wait...you're saying that the results say that the universe is finite but unbound?




#4
Nov1012, 11:15 PM

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New cosmic model parameters from South Pole TelescopeWhat do you mean by "unbound"? In normal cosmology space is boundaryless so the positive curvature case typically means something like the 3sphere. 



#6
Nov1112, 12:11 AM

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overall positive curvature curvature must be measured from inside the space since there is no outside and it may (or may not) expand indefinitely. if the cosmological constant is that, is as it seems to be from observations, then it will expand indefinitely. ================= so the picture one gets from the SPT report is very much analogous to the 2D balloon surface world, an expanding hollow 2sphere, not embedded in any surrounding space, all existence concentrated on that finite area. Like that analogy except a 3D version of it. A boundaryless finite volume 3D space that you can circumnavigate. That has a constant positive curvature experienced (for example) by triangles adding up to more than 180 degrees, how much more depending on size, positive curvature experienced from within the space IOW. I don't know how much of this is familiar to you already, I guess a lot. But it is possible you have more questions, if so please ask. The sad thing is that the SPT report may get contradicted by another report that studied much more nearby stuff, Spitzer telescope, Wendy Freedman and Barry Madore et al. I don't know how this will play out. Sean Carroll liked the SPT report, so do I. But some new supernovae data may affect the next iteration. I am in suspense as to whether this confidence interval for the curvature gets confirmed and "gels" so to speak. I want it to. Its really neat to have a finite volume boundaryless universe. But we have to wait and see. 



#7
Nov1112, 12:28 AM

PF Gold
P: 11,055

Yes, this result is freakin cool. Of course, any result that says one way or another what shape and size our universe may be is freakin cool!




#8
Nov1112, 12:50 PM

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From page 14 of the paper 
"... The tightest constraint on the mean curvature that we consider comes from combining the CMB, H0, and BAO datasets: k = 0:0059 +/ 0.0040 : (21) While the CMB+BAO constraint shows a 2.0 sigma preference for k < 0, the significance of this preference decreases as more data are added. The tightest constraint, coming from CMB+H0+BAO, is consistent with zero mean curvature at 1.5 sigma. ..." The case for a closed universe looks promising but, not yet compelling, IMO. 



#10
Nov1212, 03:43 PM

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But we'll see which way Nature herself inclines. 



#11
Nov1312, 06:09 AM

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#12
Nov1312, 09:47 AM

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==quote page 14 of SPT report== CMB lensing enables an independent constraint on curvature, although the most powerful curvature constraints still come from combining CMB data with other lowredshift probes (e.g., H_{0}, BAO). The curvature constraint using CMB+H_{0} data is Ω_{k} = 0.0018 ± 0.0048, while the constraint using CMB+BAO data is Ω_{k} = −0.0089 ± 0.0043. The tightest constraint on the mean curvature that we consider comes from combining the CMB, H0 , and BAO datasets: Ω_{k} =−0.0059±0.0040. (21) ==endquote== The tightest constraint, they say, came from including all three types and that is what equation 21 is based on. It is how it should be if the data is sound, including more gives more reliable results, and it represents scientific integrity (rather than "cheating") to include more. It seems to be the opposite of "cherrypicking." Do you understand my reasoning here? 



#13
Jan513, 12:01 AM

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I found this thread after reading http://www.physicsforums.com/showthread.php?t=662146, where marcus reiterated the conclusion that a combined fit suggests nonzero mean curvature. This is an old thread, but my post makes more sense here.
It's important to look at the most recent SPT paper 1212.6267 to get a better handle on this. There, they do likelihood estimates for various extensions of [itex]\Lambda\text{CDM}[/itex] models. Table 2 presents the oneparameter model where mean curvature is added. The improvement in fit provided by curvature is completely negligible for WMAP+SPT and substantially below 2[itex]\sigma[/itex] for WMAP+SPT+BAO+[itex]H_0[/itex]. This is marginally insignificant. The next set of observations involves extension involving nonzero neutrino masses, for which we have independent confirmations. There, both combined data sets also show less than 2[itex]\sigma[/itex] improvements. In particular, while WMAP+SPT shows a marginally insignificant improvement for adding [itex]m_\nu[/itex], the addition of the lowredshift data raises the significance by a considerable fraction. Furthermore, if we look at the 2parameter extensions that are included in that table, the neutrino mass plus number of effective neutrino species model appears to be significant above 2[itex]\sigma[/itex] when low [itex]z[/itex] is added. While it's not in that table, the 2parameter model with neutrino mass and curvature is discussed at the bottom of section 6.3. We're told that adding curvature to the neutrino mass extension "reduces the preference for massive neutrinos to 1.7σ." Finally, it's important to look at section 4, where they discuss the consistency between the WMAP+SPT and lowredshift BAO+[itex]H_0[/itex] data sets. An important graphic is Fig 2, showing contours for the dilated comoving distance vs the Hubble constant. In the rightmost graph, the colored bubble is WMAP+SPT, while the BAO+[itex]H_0[/itex] data is in greyscale. We see that there is a greater than 2σ gap between the two combined data sets. The paper remarks that "We find the apparent tension significant enough in some model spaces, including [itex]\Lambda\text{CDM}[/itex], to suggest caution in interpretation of the results. However, in no model spaces is the significance sufficient to rule out statistical fluctuations, and we have no evidence for either systematic biases or underestimated uncertinties in the data." It seems that the low statistical significance of the mean curvature extensions combined with the apparent problems in combining these data sets suggests that it's much too early to conclude that nonzero mean curvature is preferred. 



#14
Jan513, 09:58 AM

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My point is it's much too early to pretend that perfectly flat exactly zero curvature is preferred




#15
Mar2313, 09:53 AM

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Reading the Hou paper, the thing that struck me most was how much degeneracy remains in the parameters. If a nonzero neutrino mass and the six sigma detection of a running spectral index are accepted, I think the detection of curvature virtually dissapears, but that's not a combination they analyse. The value of Neff also seems to come out closer to 3.7 in WMAP and Hou and throwing that into the mix complicates it further.
One thing is clear, patience is required! 



#16
Mar2313, 12:19 PM

P: 2,896

Also I have to admit like Marcus that I'm geometrically attracted towards the hypersphere, maybe influenced by Einstein early model that had this spatial geometry (of course his had constant radius unlike what would be the case with our universe). 



#17
Mar2313, 01:39 PM

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We cannot infer from a null result that our hypothesis is nevertheless true, but just too small an effect to have measured. "Common sense" should not be confused with the scientific method, instead it usually involves the absence of scientific reasoning. While it is correct to say that the data do not rule out a small curvature, it is incorrect to say that the data suggest a nonzero curvature. This is an extremely important point that one of the experimentalists around here would do much more justice to. My specific objection was to the part of marcus' statement 



#18
Mar2313, 03:05 PM

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Out of all possible numbers, pretending that the curvature is EXACTLY zero is a really radical assumption. That has always been the hypothesis that one would look for evidence to support. The null hypothesis is, of course, that it is not exactly zero.
I think there is insufficient reason to claim exact zero perfect flat. As I said it is much too early to assume that. I have never claimed that the curvature is nonzero, although I've pointed out that some observations SUGGEST this. I just don't think there is a valid scientific reason to believe exact zero out of all the things it could be. Back in October the SPT report had an Omega_k confidence interval that was all on the negative side! It did not even include zero. Of course other studies have published Omega_k confidence intervals that include zero and some positive territory. But in recent years they've mostly been lopsided (big on the negative side of zero). That PROVES nothing. But it is suggestive when it happens repeatedly with several different studies. So, we will wait and see. 


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