What does observable universe mean? I saw your graphs in proper and comoving distances. An hypothetical object that emitted light at the Big Bang (after recombination: cosmological time $t=0$ and proper distance close to 0 with respect to our world line) is now at a proper=comoving distance (since now $a=1$) of 46 billion light years away from us (particle horizons). But do we see it now as if it had been 46 billion light years away from us at time $t = 0$? (light cone in comoving distance).
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