What is the furthest thing we can see at the time the light was emitted?

Question

To be more precise, let $P$ denote the position where the Earth is at the time this post is submitted. Assume our coordinate system is such that this point is fixed in space and the rest of the universe is expanding away from it. Therefore, by the time you are reading this, Earth will have already left $P$ due to it orbiting the Sun and the rotation of the Milky Way etc. However, this distance is negligible on cosmological length scales.

So more precisely, my question is: which objects were the furthest away at the time they sent/emitted light which have reached $P$?

I believe the cosmic microwave background (CMB) radiation is the oldest light to reach $P$. The universe was approximately 379,000 years old when the particles emitted the light that makes up the CMB. However, the universe was much smaller (or denser if the universe is infinite) at the time that light was emitted. Therefore, $P$ and the particles that emitted the CMB light, were actually quite close together (on cosmological length scales)? It depends on how much the universe expanded in the first 379,000 years, but I'm not sure what to 'google' to find that out.

Therefore, the most distance light (at the time the light was emitted) is not the oldest light?

Answer 1

If we consider hydrogen recombination to be completed by 50% then the red shift, or z is equal 1500, if hydrogen recombination to be completed by 90% then z is 1070.

This has happened much later than recombination of helium, so in terms of what we can see we can ignore earlier helium recomination.

This is from here https://en.m.wikipedia.org/wiki/Recombination_(cosmology)

As universe gets older and recombination becomes more complete, we can see further, the CMB that we can see has z equal to 1089, a bit more than 90% recombination.

https://astro.ucla.edu/~wright/CosmoCalc.html

Then here you could plug these numbers and get universe age, distance, and more. For z 1089, H0 69.6, omega 0.286, omega vac 0.714, distance is 45.5 billion light years

But it is all approximate, because we dont even have a good result for the universe expansion speed - hubble constant. Direct and indirect results differ by 15%, and you will have to live with this error.

https://en.m.wikipedia.org/wiki/Hubble%27s_law

We also dont have any idea about how the hubble constant changes with time. The deceleration parameter, that is especially important in trying to determine something that uses hubble constant far back into the past or future. High and low estimate differ by 50%. It doesnt affect the calculation as much, but it is just to show that our ability to precisely predict such distant times is not great.

https://en.m.wikipedia.org/wiki/Deceleration_parameter

Distance could be estimated by comparing the speed of object moving away and the hubble constant.

distance = speed / hubble constant

Hubble constant 69.6 km/s per mps

Megaparsec is 3261563 light years

Speed of light is 299792 km/s

I got 51.03 billion light years for z 1089, assuming speed is just that multiplied by the speed of light. This is the distance right now. You asked about the distance when light was emitted. Assuming agakn that hubble constant doesnt change, we could do this:

distance then = distance now - hubble constant multiply by time passed

But uncertainty in universe's age is 59 million years, while age of universe at that time is less than 1 million years, so we cant use this method.

https://astro.ucla.edu/~wright/distance.htm

So my answer is useless. But hey, someone asked this question and got an answer. Their answer is 84.6 million light years for a similar date or red shift

Size of universe after inflation?

Upd: radius, and distance, is half of that, 42.3 million light years

Answer 2

What we notice as the CMB is the oldest observable 'light' in the universe, and what is notable about it is that it is constant in every direction no matter where you observe from. We see it as microwave radiation now, as the expansion of the universe has redshifted (z=1100) the wavelength from what was originally infrared blackbody radiation (T~3500K) to now microwave lengths.

Just after the big bang, photons were coupled to matter in a hot dense plasma of photons, electrons, and protons. After photons decoupled from matter due to expansion and cooling in the universe, (the time of 'recombination') these photons could travel freely through space, and interact with matter. These were the first observable photons, and indeed what we see as the CMB today.