How is universe curvature measured?

  1. Feb 2, 2012 #1
    I just want to ask, because it is easy to imagine on small scale (eg draw triangle on small sphere and than make sum of its angles). But how it is really done at universe scale, when we cannot leave our position to see the big picture?
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  3. Feb 2, 2012 #2


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    The most recent efforts to measure curvature have included supernova, CMB anisotropy, and giant void studies. Supernova make good 'standard candles' because they are phenomenally bright and believed to have uniform peak luminosity. Unfortunately, even supernova are difficult to detect beyond about z=2, which is a pretty small slice of a universe that is observable out to about z=1100 [CMB]. The cosmic microwave background (CMB) is known to be highly sensitive to spatial curvature of the universe. By measuring small angle fluctuations in the temperature of the CMS, curvature near the surface of last scattering can be estimated. Giant void studies attempt to model supernovae observations without resorting to dark energy. Some of these models are compatible with the small angle CMB measurements, but, the voids must be peculiarly deep and empty, or the universe is positively curved. Older methods have included galactic surveys, relying on the size of the largest galaxies or their numerial density in any given volume of space. The error margins of such these methods are large for a number of reasons. All of the measurement methods tried to date have proven inconclusive. All we can say at this point is they are not inconsistent with a flat Universe.
    Last edited: Feb 2, 2012
  4. Feb 3, 2012 #3
    Chronos, you mentioned that supernovae are only observable up to ~ z=2 yet the CMBR is of course observable at z=1100. How is that the photons from a high intensity event such as a supernovae are attenuated so much, yet the photons from the 3000K (or is it 5000K) BB last scattering hydrogen gas (ie. much lower energy) can still reach us? Is it related to different interstelar medium attenuations for different photon frequencies?
  5. Feb 3, 2012 #4
    Imagine trying to observe the CMB if it only existed as a single point in the sky the size of a z=2 supernova.
  6. Feb 3, 2012 #5


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    The link below is a really good paper that combines the supernova data, the data from the CMB, and the data from baryon acoustic oscillations (BAO) all in one analysis. These are three completely different types of measurements, and the fact that they are all consistent with one another really gives confidence to the Lambda-CDM standard cosmology model. You can see in Figure 5 that the data are quite consistent with a flat universe. If there is large-scale curvature, it is quite small - less that about 0.02 (see Table 7).
  7. Feb 4, 2012 #6
    Chronos, that's an excellent synopsis on measuring space curvature.
    Last edited: Feb 4, 2012
  8. Feb 4, 2012 #7
    Thank you. That's what I have been looking for.
    However I have troubles in understanding the logic behind those conclusions. I have found some papers about those measurements, but I am lost within them. Is there some review of what results and why are expected for different univerese curvatures?
  9. Feb 4, 2012 #8


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    I am unaware of any single source for this information. The most critical test to date is the small scale anisotropy of the CMB. Here is a reference The problem with all of these methods is they rely on assumptions. This is a common issue in science. Every theory is forced to rely on assumptions we believe 'true', but, are not proven beyond any reasonable doubt. By testing our theories, we also test the underlying assumptions. If a pattern emerges that casts doubt on a fundamental assumption, new physics is a possible outcome. That is also the beauty of science, we never know where the next great discovery may originate.
  10. Feb 5, 2012 #9
    Thank you. I am trying to get insight how curvature is measured, simply because I do not like flat universe idea. So I want to know how it is measured and what assumptions are made to be able make up my mind.
  11. Feb 5, 2012 #10
    Keep in mind that even if the observable universe is measured as flat it doesn't prove anything conclusively other than that the observable universe is flat. The wider universe may be curved still, yet so vast that even a 90 Gly region seems flat. Or it may be the wider universe is entirely flat, regardless. People have differing opinions on what's out there.
  12. Feb 6, 2012 #11
    Yes, I thought about that, but I also understood that supernova radiation significantly outshines the total output of a whole galaxy and yet we can see galaxies out to z=8.6.
    So the size of the supernova would have to contribute greatly in preventing supernova from being detected > z=2

    I believe that Pop III stars had very short explosive lives. Here are some interesting wiki references on this:

    "The yet-to-be-observed first light from the oldest Population III stars, not long after atoms first formed and the CMB ceased to be absorbed almost completely, may have redshifts in the range of 20 < z < 100"

    "Because of their high mass, current stellar models show that Population III stars would have soon exhausted their fuel and exploded in extremely energetic pair-instability supernovae. Those explosions would have thoroughly dispersed their material, ejecting metals throughout the universe to be incorporated into the later generations of stars that are observed today. The high mass of the first stars is used to explain why, as of 2010[update], no Population III stars have been observed. Because they were all destroyed in supernovae in the early universe, Population III stars should only be seen in faraway galaxies whose light originated much earlier in the history of the universe, and searching for these stars or establishing their nonexistence (thereby invalidating the current model) is an active area of research in astronomy."
    Last edited: Feb 6, 2012
  13. Feb 8, 2012 #12
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