Size of the early universe as we see now

[stuart100]

TL;DR

In a spherical view from earth, the distant objects occupy a larger surface that closer ones. This at first thought suggests it was a bigger volume.

Don't sleep much, so I'm thinking...As we look further away at light that took billions of years to reach us, I guess all of that region is nowadays much bigger, only we wait for that light from their "now" to get to us. If our local universe can be styled a sphere obviously the further away the more spread-out (stretched) that old location would appear to be. We see the past from every direction. Otherwise, the earlier universe was bigger than now. So, is there a distortion of our view such that length towards us shrinks so that profile increases co-respondingly? Also, could is be that the space of the past shrinks relatively to current space instead of the other way round?

 

[Ibix]

Eyeballing the uppermost graph in figure 1 of Davis and Lineweaver, which has proper distance on the horizontal scale, the lightcone stops expanding and starts shrinking about 10 billion years ago. That means that when we look at things older than that and consider two thin spherical shells, one just outside the other, the outer one was smaller at the time it emitted than the inner one was at the time it emitted. I think that's what you're getting at.

That will affect things like the predicted number density of objects at different redshifts. I don't think it would affect radial distance measurement, although that probably depends in what sense you are thinking of measuring it (distance is a complex topic in cosmology).

Also, could is be that the space of the past shrinks relatively to current space instead of the other way round?

You can view it that way if you like. Since we typically set the scale factor to 1 in the current epoch one could argue that we do already. The choice won't make any difference to anything physical.