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If I understand correctly, then the surface of last scattering (the last particles off of which CMB photons scattered before traveling for 13 billion years and reaching us) is currently at a distance of around 42 billion lightyears from us, just before the particle horizon.

How far away was this surface at the moment of recombination?

Also, when we calculate the curvature of the universe by comparing standard rulers on the CMB to their measured angular sizes, which distance do we use as the "distance to object"? Do we use the distance described in this question, or the distance to the particle horizon, or some other distance?

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The distance to the surface of last scattering was 0 at the moment of recombination.

The distance of last scattering (the raius of the surface of last scattering) at any time is the distance from which the recombination radiation (which today is the CMB) can have traveled since the time of recombination. Since that time was zero at the time of recombination, that distance must also have been zero.

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  • $\begingroup$ I think you misunderstood my question. I don't mean how far had the CMB photons traveled at the moment of recombination; I mean how far from us was the surface of last scattering at that moment? The time taken for those photons to reach us was not zero, as you suggest, but rather (the age of the universe) – (time between Big Bang and recombination). $\endgroup$ – WillG May 8 '19 at 22:31
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    $\begingroup$ But that's what the surface of last scattering is - a sphere with radius determined by how far the CMB has traveled since emission. If you are asking how big the current surface of last scattering was when the CMB was emitted, just divide its current size by the redshift of the CMB, around 1100. But that's not really a physically meaningful quantity. $\endgroup$ – Thriveth May 9 '19 at 2:55
  • $\begingroup$ But isn't it meaningful in the sense described by my third paragraph? $\endgroup$ – WillG May 9 '19 at 16:55
  • $\begingroup$ I too think you have misunderstood this important question. What was the radius of last scattering at the time of last scattering ? $\endgroup$ – cumfy Feb 19 at 2:16
  • $\begingroup$ @cumfy what exactly is it you think I did not understand in the question you just repeated without adding anything? $\endgroup$ – Thriveth Feb 19 at 8:37

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