# Confusion on co-moving distance and the Big Bang

I'm at sea. From the wiki. entry https://en.wikipedia.org/wiki/Comoving_and_proper_distances : “..Most textbooks and research papers define the comoving distance between comoving observers to be a fixed unchanging quantity independent of time, while calling the dynamic, changing distance between them "proper distance”..” My confusion: Two galaxies having a comoving distance of, say, 1/2 billion LY, according to the entry, have this as a fixed distance for ALL time. But how do I reconcile that there was a time when their comoving distance could easily have been 1/100th or 1/1000th that distance, closer to the Big Bang?

## 1 Answer

How do I reconcile that there was a time when their comoving distance could easily have been 1/100th or 1/1000th that distance, closer to the Big Bang?

There's really nothing to reconcile. If two bodies have the same velocity relative to the Hubble flow, that is, their only motion relative to each other is the motion due to the expansion of space, then the comoving distance between them is fixed for all time.

The proper distance between your two galaxies was certainly smaller when they were young, but the comoving distance was exactly the same as it is today, by the definition of comoving distance.

That may seem a bit strange, but comoving coordinates are just another set of coordinates, and in General Relativity there is no privileged system of coordinates: we're relatively free to define whatever coordinate systems that are convenient. In cosmology, when you want to ignore the Hubble flow, comoving coordinates are rather convenient.

For more info about coordinate systems in General Relativity, please see Wikipedia's articles linked at Category:Coordinate charts in general relativity; there are also numerous related questions and answers on this site.

• BTW, you may enjoy this popular article on expansion by Tamara Davis & Charles Lineweaver. They have a formal paper on the topic here. – PM 2Ring Aug 25 at 21:47