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I know that something that was originally ~14 billion lightyears away is now ~46 billion lightyears away due to the expansion of space. I don't understand how the light is able to reach us in 14 billion years if the distance between us and the object has increased. I have seen a number of explanations that address how space can expand faster than light, but none seem to address my question.

Time = distance / velocity. If the velocity is constant (speed of light) and the distance is strictly increasing, then the time must strictly increase as well. Along the photon's path towards us, the distance is indeed strictly increasing (the rate of expansion changes, but the distances still increases). How then can the photon reach us in 14 billion years if it started 14 billion years away and the distance it must travel increased during that time?

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  • $\begingroup$ Light from a 4 billion year old object reaches us in a matter of minutes... $\endgroup$
    – Jon Custer
    Jul 25, 2022 at 17:28
  • $\begingroup$ But it is only light-minutes away. How can the light from something that started at 14 billion light years away reach us in 14 billion years? $\endgroup$
    – theta
    Jul 25, 2022 at 17:30
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    $\begingroup$ Who says it started 14 billion years away? $\endgroup$
    – BowlOfRed
    Jul 25, 2022 at 17:46

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It wasn't 14 billion light years away when the light was emitted. It was much closer.

The universe is 13.7 billion years old. No light has been travelling for 14 billion years. Let's assume you were rounding up. Suppose we have an object at redshift of 20. Using conventional cosmological parameters, this corresponds to the light being emitted about 13.5 billion years ago and a (current) comoving radial distance of about 36 billion light years.

However, the scale factor of the universe at $z=20$ is $1/21$, so the comoving distance when the light was emitted was about $36/21 = 1.7$ billion light years.

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  • $\begingroup$ Really nice answer. Does this mean that the edge of the observable universe was 0.2Bn years after the big bang, at about 1.7 Bn light years away? $\endgroup$ Jul 29, 2022 at 20:21

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