Why does the early universe look so big in a telescope? [duplicate]

As we look into the Deep Field, we see the Hubble photos of early galaxies up to only $400$ millions years old:

Wikipedia: List of the most distant astronomical objects

Because there is no center of the universe expansion, we can look for early galaxies anywhere in the sky. The earliest galaxies appear to us as the most distant in every direction. Therefore the early universe appears from our viewpoint as the most distant and thus the largest sphere with the radius, as we see it, of $13.4$ billion light-years (based on the most distant object in the above Wikipedia link).

Oversimplifying the spacetime geometry for a moment, the circumference of the early universe appears to us as $84$ billion light years ($2\pi\cdot 13.4$) at the age of only $400$ million years. Clearly this calculation is incorrect. Obviously the universe was much smaller. However, we can see numerous galaxies along this circumference of our viewpoint. So either the distances we see between the early galaxies are much smaller than they appear to us in the sky or else the early universe looks way too big for its age.

What is the logical explanation of this illusion?

EDIT

This question is about the paradox that the distant galaxies appear magnified. Obviously, it is different from "where the Big Bang happened". I have provided the correct answer below.

marked as duplicate by Jon Custer, heather, peterh, Daniel Griscom, mpvSep 27 '17 at 13:25

For the record: the question is based on a misapprehension of the FLRW model.

The model assumes the universe is isotropic and homogeneous, and homogeneity requires the density of matter to be the same everywhere. If the universe is infinite, which is not ruled out by observation, then it contains an infinite amount of matter all at the same (average) density. Since measurements show the universe is spatially flat, for any radial distance $r$ the universe contains a circular path of circumference $2\pi r$, though for $r \gt 13.7$ billion light years that circle is too far away for us to see. The circular path referred to in the question just happens to be the farthest such path currently observable.

As we go back in time the density of matter increases but remains constant everywhere. The Big Bang would therefore have an infinite amount of infinitely dense matter. However it is widely believed that some quantum gravity effect would become important at the very densities close to the Big Bang and this would stop the density from becoming infinite.

• @safesphere you're missing an important qualifier: the observable universe, which is finite, would be a point at the big bang, not the whole universe. – Johnathan Gross Sep 18 '17 at 13:06

That isn't how you calculate the size of the early universe. It's just the circumference of a circle with a radius of 13.4 billion lightyears. That's not even a good measure of the universe's size anyway. We don't actually know the size of the universe. All we can see is the part of the universe that is within the Earth's past light cone.

Since the universe is 13.4 billion years old, that creates an apparent sphere of radius 13.4 billion lightyears that we can see. This is called the observable universe. Because of the universe's expansion, what we saw 400,000 years after the big bang as the CMB has expanded out to a sphere of radius 46.5 billion lightyears. Using the same expansion math, we can say that the size of the observable universe at the time it was emitted was only 43 million light years. (Wikipedia Source)

• Comments are not for extended discussion; this conversation has been moved to chat. – ACuriousMind Sep 18 '17 at 16:09

Found the correct answer with a full mathematical treatment. Despite a lack of understanding from the responders, the issue in the question was stated correctly: more distant galaxies do indeed appear magnified. The following reference describes why (essentially the same reason as stated in my question) and provides the calculated visible size for all 3 possible space curvatures for the open or closed universe.

Computing the size of the observable Universe - Cosmological Horizon and Angular Diameter Distance