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Does the mapping of CMBR measure spatial flatness or spacetime flatness of the universe?
Does the mapping of CMBR measure spatial flatness or spacetime flatness of the universe?
Could you clarify the difference between intrinsic and extrinsic curvature?zero intrinsic curvature, but they non-zero extrinsic curvature
Your initial question has been answered already, but I thought I'd add something:Does the mapping of CMBR measure spatial flatness or spacetime flatness of the universe?
I didn't realize this. So to what extent can non-flatness resolve the H0 tension? I notice in the H0LiCOW thread that assuming slightly negative curvature of 0.01 resolves about half of the disconnect. So what keeps one from going further? If Ωk = -0.02, does that resolve the whole disconnect? There must be other constraints that prevent one from moving it that direction.The CMBR measurements don't actually measure space to be flat on their own. There is a degeneracy between the rate of spatial expansion and spatial curvature. Measurements from the nearby universe resolve this degeneracy. So it's the combination of CMBR and nearby measurements that show the universe as being spatially-flat, with Baryon Acoustic Oscillations being the most common and highest-precision.
My understanding is that the tension in expansion rate could be entirely resolved by having a slightly non-flat universe. But I'm not 100% sure on that, as I haven't looked at it in detail. But I seem to remember it being explicitly mentioned as a possible explanation in the papers pointing out the discrepancy.I didn't realize this. So to what extent can non-flatness resolve the H0 tension? I notice in the H0LiCOW thread that assuming slightly negative curvature of 0.01 resolves about half of the disconnect. So what keeps one from going further? If Ωk = -0.02, does that resolve the whole disconnect? There must be other constraints that prevent one from moving it that direction.
Could you clarify what is meant by 'degeneracy' between the rate of spatial expansion and spatial curvature?There is a degeneracy between the rate of spatial expansion and spatial curvature.
Fig. 29 (page 40) of this paper shows the degeneracy:Could you clarify what is meant by 'degeneracy' between the rate of spatial expansion and spatial curvature?
So degeneracy essentially means that the correlation between ##\Omega_k## and ##H_0## and ##\Omega_m## is weakened.Fig. 29 (page 40) of this paper shows the degeneracy:
https://arxiv.org/abs/1807.06209
It's a little more complicated, as the matter density fraction is also a part of it. The basic way to understand this is that the CMB data very tightly constrains ##H_0^2 \Omega_m## (this is the matter density), but curvature is largely (though not entirely) degenerate with both ##H_0## and ##\Omega_m##. So if the curvature parameter is off, then you get a different median estimate for both curvature and matter density fraction.
Interesting, though, is the fact that even with this degeneracy, the CMB data really has a hard time fitting the higher nearby estimates of ##H_0## (it permits lower values of ##H_0##, but not higher). So the tension is more significant than I thought in my earlier post, after looking at the most recent data available in that paper.
Sort of. A degeneracy means that given two of these values, you can extract the third with relatively high precision. A complete degeneracy would mean that given two values, the third is exactly-specified. An approximate degeneracy, as in this case, just means that given two of them, the third is tightly-constrained. Such approximate degeneracies are very common in observational science.So degeneracy essentially means that the correlation between ##\Omega_k## and ##H_0## and ##\Omega_m## is weakened.
Hi kimbyd:So it's the combination of CMBR and nearby measurements that show the universe as being spatially-flat, with Baryon Acoustic Oscillations being the most common and highest-precision.
Yup. That's an accurate way to state it.Hi kimbyd:
I am wondering if you might agree that the following is an acceptable rephrasing of the quote above.
So it's the combination of CMBR and nearby measurements that show the universe as being so close to spatially-flat that current methods of analysis are not able to distinguish it from non-flatness, with Baryon Acoustic Oscillations being the most common and highest-precision.My understanding is that the current uncertainty of the value of Ω_{k} allows for about a 10% possibility that |Ω_{k}| might be larger than 0.005.
Reference:
Regards,
Buzz