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Ok, I know this has been asked by a lot of people, but my reason for asking this question is a bit different. Please read further.

I was watching a video by Fermilab (Start at 6:30, at 8:30 he mentions how we cannot ever see light emitted from objects > 14bn light years away). In it, the presenter Dr. Don Lincoln talks about the speed of light and how some things are faster than that. Expansion of the Universe can be faster than the speed of light, because galaxies 1 megaparsec away appear to be moving at the rate of 68km/s, galaxies 2 megaparsecs away at 136km/s, and so on. So the velocity of the galaxies doubles every megaparsec. If we do the math, the speed of the galaxies moving away surpasses the speed of light at 14 billion light years away.

14 billion is just 200 million give or take more than the current measurement of the age of the Universe.

My question is, at 14 bn light years away the galaxies are moving faster than the speed of light and we can never see anything beyond that ever. Does this mean that even after say 5 billion years (assuming we still exist), if somebody uses the same technique to measure the age of the Universe, they will end up with the same number that is lesser than 14 billion?

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    $\begingroup$ We can certainly see things beyond that. The most distant confirmed galaxy GN-z11 has a proper distance of 32 billion light years, at a red shift of about 11. It has a light travel distance of 13.4 billion light years. Not the same as the proper distance due to the expansion of space over those 13.4 billion years. $\endgroup$
    – James K
    Jan 4, 2021 at 10:12
  • $\begingroup$ Related: astronomy.stackexchange.com/a/19910/16685 $\endgroup$
    – PM 2Ring
    Jan 4, 2021 at 15:37
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    $\begingroup$ For the sake of completeness, the mentioned video should be referenced in the question. $\endgroup$
    – lordparthurnaax
    Jan 4, 2021 at 15:48
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    $\begingroup$ No, it is calculated into. The distance of the things what we see 13.7bln ly away, are now 46bln ly away. It is not a simple doubling in every X years, there is a more complex curve (for example, the expansion of the Universe decelerated in its first 8bln years, since then it accelerates). Note, we have no way to know things about the future, we only can extrapolate the current processes. Maybe once it will decelerate again, who knows? This all is absolutely not so sure like math. $\endgroup$
    – peterh
    Jan 4, 2021 at 16:55
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    $\begingroup$ @lordparthurnaax I have now added the link to the video with the timestamp to look at. Thanks! $\endgroup$
    – Deepak Kamat
    Jan 4, 2021 at 17:05

2 Answers 2

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The age of the universe is not calculated based on the size of the visible universe. The age of the universe is being calculated based on the fact that the laws of nature have no direction. This means that you can use the laws of nature to predict future behavior, but also assume previous behavior. Based on calculating backwards with the laws of nature, for instance, general relativity, physicists can to a pretty certain degree calculate backwards how the universe started.

The fact that the universe is expanding and the size of the universe is what it is, has no relation to the age of the universe. Please, look at another video from Don Lincoln about the size of the universe and its age. Here it is explained that the universe already had an extra large expansion making it bigger than the age.

What will happen, though, is that the visible universe, which is smaller as the actual size of the universe, will be more empty over the course of time. In the 5 billion years you mentioned, there will be more galaxies outside the visible boundaries of the universe, because they are moving away from us faster than the speed of light. The expansion of the universe, hypothesized due to dark energy, makes the universe bigger, not older.

If the laws of nature don't drastically change, and we use these laws in 5 billion years to calculate the age of the universe, we should end up with the right number, 14 billion plus 5 billion years.

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There are many extremely widespread misconceptions about cosmology. One is the idea that there's some importance to cosmological recession speeds larger than $c$. In reality, recessional speeds are defined in a somewhat peculiar way and the value $c$ has no significance in them. It's not a limiting speed, and it's not in any useful sense "the speed of light". It's possible to have two galaxies with a recessional speed that is, always has been, and always will be larger than $c$, that can still communicate with each other by light-speed signals. In a homogeneous sub-critical density universe with zero cosmological constant, for any speed $v$ no matter how large, there are galaxies with a recessional speed always larger than $v$ that can communicate back and forth an infinite number of times. (To be fair, the signal will be very faint, and they'll have to wait very long for the reply—but not forever.)

In the video that you linked, the speaker correctly notes (at around 7:44) that with the current value of the Hubble constant, the solution of $H_0 d = c$ is $d\approx 14\text{ billion light years}$. This distance even has a name, the "Hubble distance", but it doesn't mean anything. It is not the limit of how far we can see. There are several ways of defining a limit of that sort but none of them give you a value of $c/H_0$. The illustration starting at 8:17, supposedly showing why light emitted beyond the Hubble distance can never reach Earth, is absolutely wrong.

That the current Hubble distance is close to $c$ times the current age of the universe is coincidence. It happens to be true in this cosmological era, but it wasn't true in the past and won't be in the future (if standard cosmology is correct).

You shouldn't learn cosmology from this guy since he doesn't understand it himself. It's very difficult to find popularizations of cosmology made by people who actually know what they're talking about. The best I've ever seen is Ned Wright's tutorial.

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