What "space" is used in defining cosmological distributions?

[Stephen Tashi]

TL;DR

What definition of "space" is used when defining spatial distributions of things in cosmology?

I assume 3-D cartesian space is not an adequate description for things at the cosmological scale. So what definition of "space" is used when people talk about things like the distribution of hydrogen atoms "in the universe"?

 

[PeterDonis]

What definition of "space" is used when defining spatial distributions of things in cosmology?

A spacelike slice of constant time in standard cosmological coordinates.

I assume 3-D cartesian space is not an adequate description for things at the cosmological scale.

It is if the universe is spatially flat, which, according to our best current model, it is.