If the oldest galaxy ever discovered, i.e GLASS-z13, is at a present proper distance of around 33 billion ly from Earth, why then do we define the observable universe to have a radius of around 46 billion ly? Is there anything currently 46 billion ly away from Earth that we can see?
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1$\begingroup$ related and with a helpful answer What Is The Maximum Distance Our Finest Instruments Could See When They're Perfected? $\endgroup$– uhohJul 24, 2022 at 13:43
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1$\begingroup$ Why do you assume that observed and observable are the same thing? $\endgroup$– JBentleyJul 25, 2022 at 10:37
2 Answers
The CMBR came from a sphere of matter with an extrapolated comoving radius of around 46 billion ly. That's the most distant thing we can see. The observable universe is sometimes defined to end there, because it's the limit of light-based astronomy, or is sometimes defined to extend back to the end of inflation, but the difference in comoving radius between the two is only one or two percent.
The distance to the most distant galaxy seen by a telescope should not be expected to converge to 46 Gly, because between the CMBR and the earliest stars there is a gap, called the Dark Ages, in which there should be nothing visible to telescopes.
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3$\begingroup$ Does this mean we will not ever see a galaxy or a star that is at a present proper distance of 46 Gly? And that the observable universe is defined as such considering the CMBR? $\endgroup$– WilliamJul 24, 2022 at 3:56
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3$\begingroup$ @William : No, because presumably there weren't any stars at that point (and if there were a few isolated ones, they'd be far, far too dim to see from here). The CMB though is essentially the image of the white hot hydrogen that filled the Universe in its earliest days, so it is still a picture of "something", technically. $\endgroup$ Jul 25, 2022 at 3:25
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1$\begingroup$ You cannot simply mention a term like "Dark Ages" and let us hanging with no more interesting info about that! What are the Dark Ages? Is that the time between when the "initiation" of the CMBR and the formation of the first galaxies? Or is it a more nefarious span of time? $\endgroup$– AnoEJul 25, 2022 at 9:25
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2$\begingroup$ @AnoE Basically the CMBR is when the hydrogen stopped being p+ and e- and started being H1. At that point the photons no longer interacted with the matter. There was then a period (the Dark Ages) during which the hydrogen collapsed into clouds, and eventually dense enough aggregations that fusion became possible - at which point the Dark Ages ended, and the first stars became visible. $\endgroup$ Jul 25, 2022 at 11:10
We don't see stars and galaxies at a proper distance of 46 Gly, because this distance corresponds to a light travel time of 13.7 billion years, or very shortly after the big bang.
When we look into the distance we also look back in time. There was a time when there were no stars. The first stars formed about 100 million years after the big bang, which corresponds to a proper distance of about 38 Gly. Beyond that we can observe the cosmic microwave background, which was emitted shortly (400,000 years) after the big bang at a proper distance of 45.5 Gly. We cannot observe before that using light (or infrared, UV, radio waves etc) because the universe was opaque to light at that time, but we could, in theory, observe events prior to this if they emitted gravitational radiation or neutrinos (as the universe would have been transparent to gravitational radiation.
So the "observable universe" is defined as going right back to the big bang at a distance of 46.4 Gly. That is the volume of space that we could, in theory, observe. Even if in practice we can't actually see anything there.
Note that the distances that I quote are the outputs of modelling the expansion of the universe, and different assumptions about how fast the universe has expanded will give different values. That is, they are theoretical distances, not directly observed distances.
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1$\begingroup$ I see two conflicting statements here, at least in my mind: First, you said a present proper distance of 46 Gly corresponds to a light travel time of 13.7 billion years. Then when you discussed the first stars, which formed 100 million years after the Big Bang (therefore having a light travel time of 13.7 billion years), you said it would correspond to a present proper distance of 38 Gly. So, does a light travel time of 13.7 billion years correspond to a present proper distance of 46 Gly or 38 Gly? $\endgroup$– WilliamJul 24, 2022 at 8:51
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1$\begingroup$ +1; I think this answers the gist of the OP's "confusion", namely that "the observable Universe" is defined theoretically, not observationally. $\endgroup$– pelaJul 24, 2022 at 15:01
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3$\begingroup$ @William A light travel time equal to the age of the Universe (i.e. 13.8 Gyr) defines the size of the observable Universe, and corresponds to a present-day distance of 46.2 Glyr (given a Planck 2018 cosmology). 100 Myr later — i.e. 13.7 Gyr ago — corresponds to a current distance of 37.7 Gyr. The CMB was emitted in between these times. $\endgroup$– pelaJul 24, 2022 at 15:07
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1$\begingroup$ @NeilBartlett They travel at the same speed as light, yes (well - neutrinos are slightly slower). The point is that before the CMBR the universe was ionized plasma, and light can't travel through that - but neutrinos and GW can. $\endgroup$ Jul 25, 2022 at 11:13
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2$\begingroup$ Not really adding to the discussion, but I love the phrase "going right back to the big bang at a distance of 46.4 GLy". The co-relation of distance and time puts me strongly in mind of the book "Inverted World", by Christopher Priest. In which the characters live on a city that constantly moves across its world. The striking opening line of the book is "I had reached the age of six hundred and fifty miles," $\endgroup$– RowanJul 25, 2022 at 11:47