How long will the CMB be detectable?

[Gerinski]

The CMB has already stretched from some 3000K to 3K, so 99.9% of all the possible stretching until asymptotically approaching absolute zero.

Even if our telescope technology continues improving, with the ongoing expansion there may come a time in the future when the CMB temperature will be so low that it may become undetectable, or at least so faint that it will not be possible to retrieve any meaningful resolution detail from it.

Do you think so? And if so, at what universe age might that start to be the case?

Could we say that we are extremely lucky to have developed the required technology for detecting and studying the CMB at an era when that is still possible? In other words, that any civilization reaching our technological level at a future age of the universe might not be able to study the CMB and therefore would have it quite more difficult to develop the cosmology of the earliest universe?

Or conversely, had we been able to study the CMB at a significantly earlier epoch of our universe, when it was still warmer, would that have enabled us to produce a much more accurate understanding of the early universe? At what temperature of the CMB could we have detected detail enough so as to unravel mysteries which may by now have become forever hidden?

Thanks,

 

[Bandersnatch]

The only comment I'll make here is that the CMBR temperature has been going down the fastest in the earliest stages of the history of the universe. The current and further expansion rates will be rather mellow by comparison. While after the first ~14 Gyrs it went down by a factor of ~1100, it'll only go down by a factor of ~2.5 after another 14 Gyrs (to approx 1K).
Here's a snapshot from Jorrie's calculator giving times for order of magnitude decreases:

Considering the numbers above, and the timescale of the technological advancement on Earth, the hypothetical future civilisations will have plenty of time to develop sufficiently precise measurements.
Other than that, the question is going to be difficult to answer, as it involves assuming something about such qualifiers as 'too faint', 'difficult', 'undetectable', etc., all while talking about civilisations whose history, biology, environment and capabilities can be pretty much anything.

 

[PeterDonis]

there may come a time in the future when the CMB temperature will be so low that it may become undetectable, or at least so faint that it will not be possible to retrieve any meaningful resolution detail from it.

As @Bandersnatch has pointed out, there probably won't be any technological reason why this will ever happen. However, if we assume that our universe will continue to be dark energy dominated forever, there is a temperature associated with our cosmological horizon, and once the CMB temperature drops to that temperature, the CMB will be effectively undetectable, not because we can't detect radiation at that temperature at all, but because we will have no way to distinguish the leftover CMB radiation from the horizon radiation. The horizon temperature, however, is much, much lower than the current CMB temperature, so it will take a long, long time for this to happen.

 

[kimbyd]

As @Bandersnatch has pointed out, there probably won't be any technological reason why this will ever happen. However, if we assume that our universe will continue to be dark energy dominated forever, there is a temperature associated with our cosmological horizon, and once the CMB temperature drops to that temperature, the CMB will be effectively undetectable, not because we can't detect radiation at that temperature at all, but because we will have no way to distinguish the leftover CMB radiation from the horizon radiation. The horizon temperature, however, is much, much lower than the current CMB temperature, so it will take a long, long time for this to happen.

For fun, I decided to do a back-of-the-envelope calculation for what this would be. Assuming I'm doing things correctly (the source I used glibly ignored units in its calculations, and decided not to say which dimensionless convention they were using), the eventual temperature of the cosmological horizon will be approximately $10^{-28}K$, which will be achieved when the scale factor is approximately $10^{28}$ times greater than it is today. If we just take the expansion rate to be a constant determined by the cosmological constant (since for most of the period in question it will be), then the expansion will follow the formula (using the convention $a(0) = 1$):

$$a(t) = e^{H_0 t}$$

Using the above formula, the CMB temperature and the horizon temparture will be the same order of magnitude in about a trillion years. According to this Wikipedia article, star formation is currently projected to cease at around 100 trillion years, indicating that there may be some civilizations which rise long after the CMB is undetectable.

 

[Gerinski]

The only comment I'll make here is that the CMBR temperature has been going down the fastest in the earliest stages of the history of the universe. The current and further expansion rates will be rather mellow by comparison. While after the first ~14 Gyrs it went down by a factor of ~1100, it'll only go down by a factor of ~2.5 after another 14 Gyrs (to approx 1K).
Here's a snapshot from Jorrie's calculator giving times for order of magnitude decreases:
View attachment 222464
Considering the numbers above, and the timescale of the technological advancement on Earth, the hypothetical future civilisations will have plenty of time to develop sufficiently precise measurements.
Other than that, the question is going to be difficult to answer, as it involves assuming something about such qualifiers as 'too faint', 'difficult', 'undetectable', etc., all while talking about civilisations whose history, biology, environment and capabilities can be pretty much anything.

Thanks to all.
Excuse my ignorance but I'm afraid I do not understand fully the figures in the chart attached, I'm just a layman. Is there any other more intuitive chart or graph showing how the CMB temperature has been dropping during the evolution of the universe, since it was emitted at some 3000K until the current 3K? (and even better if there was any projection of the expected future temperature evolution).
And, is that calculator taking into account that the expansion is accelerating?
As for the other comments I understand that a future hypothetical civilization will still be able to detect the CMB, in principle until it will become blurred with the horizon temperature some trillion years from now (I understand from your comment that such a calculation considers a steady expansion, not the actual accelerating expansion, right?).
But I guess that much before that it may well become impossible to extract useful information from the CMB. Sure we can not predict the technological achievements of such a civilization, they may be able to discern temperature gradients of thousands or millionths of a degree, but we may also conceive that their technology may only be able to discern gradients of tenths of a degree, in which case they would not be able to extract much information from the CMB.

 

[Gerinski]

By the way, I'm afraid I do not understand clearly what the source of those "horizon photons" is meant to be, which would eventually become mixed / blurred with the CMB, could any of you kindly clarify?

 

[PeterDonis]

Is there any other more intuitive chart or graph showing how the CMB temperature has been dropping during the evolution of the universe, since it was emitted at some 3000K until the current 3K?

The CMB temperature drops the same way the frequency of all photons moving freely in the universe drops because of cosmological redshift. The CMB photons are redshifted by a factor of about 1000, so the CMB temperature has dropped by the same factor. That factor is also the ratio of the scale factor of the universe now to the scale factor of the universe at the time of CMB emission. The same evolution will continue into the future.

is that calculator taking into account that the expansion is accelerating?

Yes.

I do not understand clearly what the source of those "horizon photons" is meant to be

It's radiation from the cosmological horizon (which is there because the expansion of the universe is accelerating), which is the analogue of Hawking radiation from a black hole's horizon.

 

[kimbyd]

And, is that calculator taking into account that the expansion is accelerating?

Bear in mind that the accelerated expansion is a description of how objects in our universe are moving away from one another at an accelerating rate.

The rate of expansion is decreasing (slowly), and seems to be approaching a constant value. A constant rate of expansion results in objects accelerating away from one another because the recession velocity is the rate of expansion multiplied by distance. If the rate of expansion is constant, increasing distance means increasing recession velocity.

Right now the rate of expansion is not quite constant, but it's decreasing more slowly than distances increase, resulting in an increase in recession velocity.

 

[Gerinski]

The CMB temperature drops the same way the frequency of all photons moving freely in the universe drops because of cosmological redshift. The CMB photons are redshifted by a factor of about 1000, so the CMB temperature has dropped by the same factor. That factor is also the ratio of the scale factor of the universe now to the scale factor of the universe at the time of CMB emission. The same evolution will continue into the future.

Thanks. Well I asked because Bandersnatch said that the temperature drop happened the most in the early epochs of the universe and that as the age grows the amount of redshift became proportionally smaller (or so I understood from his answer). So I understand that the temperature drop is not linear with the expansion rate, and if so that's why I asked for a more graphical way of grasping how the temperature drop evolves with the universe age, I guess it would not draw a straight sloped line but some kind of curve?.

"That factor is also the ratio of the scale factor of the universe now to the scale factor of the universe at the time of CMB emission. The same evolution will continue into the future". Yes but since the expansion is accelerating, for a layman like me who can not have a visual intuition for the scale factor evolution, it's difficult to get some understanding about how the temperature actually evolves, and will evolve, in time.

BTW, if I understand well the accelerating expansion of the universe means that spacetime coordinates which are now close to the edge of our observable universe, inhabited by some very early stars and proto-galaxies, may eventually disappear from our horizon as they cross the point where their expansion rate exceeds the speed of light from our frame of reference. If so, would not the very CMB emitting surface, the surface of last scattering, also become eventually far enough that light from it would not be able to reach us anymore because that surface would be receding from us at an FTL rate?

 

[Bandersnatch]

Excuse my ignorance but I'm afraid I do not understand fully the figures in the chart attached, I'm just a layman.

In the future, please mark threads on topics you're a beginner in as 'B'. 'I' indicates undergraduate-level prior knowledge. Thanks. :)

that's why I asked for a more graphical way of grasping how the temperature drop evolves with the universe age, I guess it would not draw a straight sloped line but some kind of curve?.

The calculator I linked to earlier (follow the hyperlink) has also graphing capabilities.
This is the relationship between temperature and the age of the universe graphed from 0 to roughly 100 billion years (that's how far the calculator can go):

Notice how the vertical axis goes only to 30 K. If you wanted the same graph but going straight to 3000 K, it'd look like this:

The calculator is a great tool for learning cosmology visually, as it can graph many more relationships. If you're interested in using it, follow the tutorial.

BTW, if I understand well the accelerating expansion of the universe means that spacetime coordinates which are now close to the edge of our observable universe, inhabited by some very early stars and proto-galaxies, may eventually disappear from our horizon as they cross the point where their expansion rate exceeds the speed of light from our frame of reference. If so, would not the very CMB emitting surface, the surface of last scattering, also become eventually far enough that light from it would not be able to reach us anymore because that surface would be receding from us at an FTL rate?

This is actually more complicated than that. The cosmic event horizon means that there exist a distance from beyond which light will never reach us, no matter how long we wait (i.e. even after infinite time). This is a feature of accelerated expansion, but it doesn't have much to do with recession velocities exceeding the numerical value equal to the speed of light. E.g. the regions from which CMBR was emitted has never been receding slower than 3c, and yet we can see them.
Furthermore, everything that once becomes observable, stays observable forever, at least in principle, and there's always more light from further away to be seen (not counting such things as being swamped by horizon radiation, or the wavelength of light becoming so stretched, that it is too large for any reasonably-sized detector). So there'll always be CMBR.

The various quirks of cosmological horizons are discussed in this article:
https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/
(best enjoyed with some maths knowledge)

 

[Gerinski]

In the future, please mark threads on topics you're a beginner in as 'B'. 'I' indicates undergraduate-level prior knowledge. Thanks. :)

Thanks a lot for the reply. I thought the difficulty level was about the question as such (as perceived by the questioner in the scope of PF in general) and not about the level of the questioner, I will follow your advice in the future, thanks!
That graph is indeed very helpful, so the CMB temperature dropped dramatically in the very early universe and has only been mildly decreasing since then, that was precisely what I was wondering.

 

[PeterDonis]

I thought the difficulty level was about the question as such (as perceived by the questioner in the scope of PF in general) and not about the level of the questioner

It can be either (or both); but generally speaking, marking a thread at a level above your own level of knowledge just means you'll get answers you can't understand. If you mark a thread based on your own knowledge level, and a topic truly can't be realistically discussed at that level, someone will generally point it out.

 

[kimbyd]

BTW, if I understand well the accelerating expansion of the universe means that spacetime coordinates which are now close to the edge of our observable universe, inhabited by some very early stars and proto-galaxies, may eventually disappear from our horizon as they cross the point where their expansion rate exceeds the speed of light from our frame of reference. If so, would not the very CMB emitting surface, the surface of last scattering, also become eventually far enough that light from it would not be able to reach us anymore because that surface would be receding from us at an FTL rate?

The CMB emitting surface (technical term: surface of last scattering) isn't an object. A galaxy, proto-galaxy, or other object is located at a particular place (though it will move over time). The surface of last scattering occurred everywhere. This surface is marked by the plasma in the early universe cooling to become a transparent gas, which occurred at a temperature of approximately 3000K, when the universe was roughly 300,000 years old. Every location in our universe cooled to this temperature. As our universe ages, the CMB which is observed stems from plasma which was cooling to a gas further away.

Perhaps a better way to think of the CMB itself is to not worry about how it was emitted, but to think of it as a photon gas.

Back before the emission of the CMB, the normal matter in the universe consisted of a hot plasma of mostly hydrogen. As a plasma is defined by its atoms being ionized, and an ionized Hydrogen atom is basically just a proton, the early universe was mostly a gas of protons, electrons, and the photons they interact with (with a good number of Helium atoms and tiny amount of other light elements thrown in). All of these were bouncing off one another all the time, exchanging energy, keeping them all together in thermal equilibrium. As this plasma cooled, the protons and electrons combined to form neutral atoms, which don't interact as readily with light. This caused the mostly-hydrogen gas and the photons to evolve independently (roughly 90% of the photons which we currently observe from the CMB never bounced off anything else in the intervening 14 billion years until they were absorbed by our detectors). So instead of a plasma, you now have a photon gas which cools as the universe expands, and a mostly-hydrogen gas which both cools and collapses to form things like galaxies.