## The Expansion of the Universe

We can wait a while to explore the Universe, but we shouldn’t wait too long. If the Universe continues its accelerating expansion as predicted by the usual model of cosmology, it will eventually expand by a factor of 2 every 12 billion years. So if we wait too long, we can’t ever reach a distant galaxy.

In fact, after 150 billion years, all galaxies outside our Local Group will become completely inaccessible, in principle by any form of transportation not faster than light!

• Toby Ord, The edges of our Universe.

This is where I got the table.

150 billion years sounds like a long time, but the smallest stars powered by fusion—the red dwarf stars, which are very plentiful—are expected to last much longer: about 10 trillion years!  So, we can imagine a technologically advanced civilization that has managed to spread over the Local Group and live near red dwarf stars, which eventually regrets that it has waited too long to expand through more of the Universe.

The Local Group is a collection of roughly 50 nearby galaxies containing about 2 trillion stars, so there’s certainly plenty to do here. It’s held together by gravity, so it won’t get stretched out by the expansion of the Universe—not, at least, until its stars slowly “boil off” due to some randomly picking up high speeds. But will happen much, much later: more than 10 quintillion years, that is, 1019 years.

### 51 Responses to The Expansion of the Universe

1. Somebody1 says:

An important issue indeed!

Just to have a data point, how far from earth will the Voyagers be in 150 billion years, assuming they don’t get destroyed or gravitationally trapped? Wikipedia says Voyager 1 will be 56 LY away in 1 million year, but does that take expansion into account? And how to go betond that? There are some references here https://space.stackexchange.com/questions/1621/where-are-pioneer-10-11-and-the-voyagers-ultimately-headed but nothing going up 150 billion years.

• John Baez says:

That’s a fun question. To answer it we need to know if Voyager is moving faster than the escape velocity for the Local Group. That is: is it moving fast enough to leave the Local Group, or will gravity pull it back in? I don’t even know if it’s moving faster than the (smaller) escape velocity for the Milky Way.

Let’s figure it out. On Astronomy StackExchange I read:

The Solar System’s orbital velocity is estimated at roughly 220 km/s, and galactic escape velocity for our vicinity at about 537 km/s. So in the direction of Solar system’s velocity vector, velocity required to escape Milky Way is ~ 317 km/s.

Some of those numbers seem suspiciously precise. But I also read that Voyager 1 is moving at 35,000 miles per hour, which is 16 kilometers/second. So even if we happened to shoot it out directly forward (in the direction of the Solar System’s motion through the Galaxy), it’s moving much too slow to ever leave the Milky Way!

• Peter Erwin says:

Wikipedia says Voyager 1 will be 56 LY away in 1 million year, but does that take expansion into account?

Yes, because there’s no expansion of space inside gravitationally bound systems like the Milky Way. (“Brooklyn is not expanding!”)

• John Baez says:

Yes, Peter is right. (I hadn’t seen that question.)

• Daniel says:

And also, the contrary is happening. We’ll be colliding with our nearest galaxy, Andromeda in.. some time.

• joel schlecht says:

The voyagers will not reach galactic escape velocity so they will orbit the center of the galaxy and never leave it unless they get flying out from some close encounter we cannot foresee in the distant future.

2. allenknutson says:

I first learned this shocking statement from Nima Arkani-Hamed, who described our children’s children in the Milky Way of some billions of years hence, who have only fairy tales left of the “other galaxies” that existed a long, long, time ago. (But did they really?) Somehow I find the idea quite depressing!

• John Baez says:

Yeah, it’s depressing. But fast-forward the universe and it gets even more depressing. From my timeline:

150 billion years from now – the Era of Isolation begins: if the accelerating expansion of the Universe continues as expected, the Local Group of galaxies including ours becomes completely isolated, with signals or spacecraft unable to reach any other galaxies.

10 trillion years from now – The smallest and longest-lived stars capable of supporting fusion today, red dwarf stars with a mass about 0.08 times that of the Sun, run out of hydrogen.

100 trillion years from now – All normal star formation processes cease. The universe settles down with a population of stars consisting of about 55% white dwarfs, 45% brown dwarfs and a small number of neutron stars and black holes. Star formation continues at a very slow rate due to collisions between brown and/or white dwarfs.

1017 years from now – All currently existing white dwarf stars cool to black dwarfs with a temperature of at most 5 Kelvin.

1019 years from now – All galaxies “boil off”, gradually losing their dead stars to intergalactic space.

1.9 × 1019 years from now – Half of all bismuth decays. All isotopes of bismuth are unstable and the most common, longest-lived one, bismuth-209 has a half-life of 1.9 × 1019 years.

3 × 1022 years from now – All binary brown dwarfs spiral in and collide due to gravitational radiation.

1.8 × 1022 years from now – Half of xenon-124 decays. This is the half-life of this isotope of xenon-124.

Given the physics I know, in the far future the main hope is that there’s something interesting you can do with black holes. But we can also hope that long before these times, some lifeform figures out a way to go beyond the physics we understand now, and do something really exciting.

• gowers says:

Are you putting in those remarks about bismuth and xenon-124 just for comparison or should I be even more depressed because twice as far into the future as the boiling off of galaxies we’ll have to make do with only half the bismuth we have now?

• Peter Erwin says:

I note that your timeline is currently missing the possible excitement $10^{1100}$ to $10^{32000}$ years in the future, when black dwarfs with masses between 1.35 and 1.16 solar masses undergo core collapse and supernova due to the cumulative effects of pycnonuclear fusion (Caplan 2020).

• Rick Sanchez says:

The Three Body trilogy does a beautiful job of exploring this idea over the course of the series and specifically touches on this last idea in the final book. Worth reading, for sure.

• John Baez says:

Gowers wrote:

Are you putting in those remarks about bismuth and xenon-124 just for comparison or should I be even more depressed because twice as far into the future as the boiling off of galaxies we’ll have to make do with only half the bismuth we have now?

Those are the radioactive elements with the longest known half-lives. 2 × 1019 years from now, the decay of bismuth nuclei may count as fun, not depressing: at least something will still be happening! We can all gather and watch the bismuth decay.

• John Baez says:

Peter wrote:

I note that your timeline is currently missing the possible excitement $10^{1100}$ to $10^{32000}$ years in the future, when black dwarfs with masses between 1.35 and 1.16 solar masses undergo core collapse and supernova due to the cumulative effects of pycnonuclear fusion (Caplan 2020).

Great! I hadn’t known about pycnonuclear fusion. An occasional supernova will provide much-needed entertainment in the time range cited.

• Chris F says:

Many people believe that humans will not be around in a couple of centuries, at the most, for one reason are another, but they can still worry about what will happen billions of years from now. People are too funny. 😂😂😂🤣

3. hansleida says:

What happens in the moment when a particular star expands out of our observable universe? From our perspective, does the light from it just wink out suddenly, or does something weirder happen?

• John Baez says:

Winking out suddenly would be too weird! As galaxies recede from us their light gets increasingly red-shifted. That is, the wavelength of the light gets stretched, so it becomes redder, and then infrared, and then microwaves, and then radio waves, and so on. And as the light gets more and more redshifted, its energy goes down in inverse proportion to its wavelength, so it gets harder and harder to detect.

I haven’t done the calculation, but I think when a galaxy falls behind the ‘cosmic horizon’ its light becomes infinitely redshifted, just like the light emitted by someone falling into a black hole. So basically as a galaxy moves away from us its light gradually gets redshifted and becomes harder and harder to detect, until eventually it’s gone.

• John Baez says:

In email Toby Ord said:

I also saw a comment on your blog regarding galaxies ceasing to be observable. What is going on there is that actually the observable universe is monotonically increasing in size, not decreasing (both in proper distance and comoving distance). So they don’t disappear across the edge. But there is a lot of popular science talking about galaxies becoming invisible. I mention this briefly in the paper. What is going on is that for distant galaxies, our past light cone never moves very far up their world line — we can only see their earliest times and never will see their later times. We get something called cosmological time dilation, where we see them slow down asymptotically and they redshift severely so that they become effectively invisible despite never leaving the observable universe and photons still arriving.

• The increase is true now, but asymptotically the Universe will approach the de Sitter model. In that model, the event horizon (not the particle horizon, which defines the observable universe) is the same as the Hubble sphere. In general, that is not the case. However, the fact that the de Sitter model was used as a fiduciary model early on might have led to some confusion here.

The late, great Wolfgang Rindler wrote the definitive paper on cosmological horizons. As always when discussing cosmology, I point out that everyone should have read Edward Harrison’s textbook Cosmology: The Science of the Universe. He has an entire chapter on horizons.

• There is also an interesting more modern paper about misunderstandings on this topic.

• There is also another good paper which clears up some confusion on these matters.

• John Baez says:

Probably most people don’t know the difference between the event horizon, the particle horizon and the Hubble sphere, which I guess is what Wikipedia calls the Hubble horizon. I can barely remember the difference myself. I’ve provided links to quick explanations.

• “Hubble horizon” is an unfortunate term, since, in general, it is not a horizon (there are special cases where it coincides with a horizon, though). The article is OK though. Think of it this way: At the big bang, imagine an expanding sphere of light (think of switching on a light bulb at the big bang). The edge of the sphere is the particle horizon. Due to symmetry, objects at the edge are the furthest objects which we can now see. For the event horizon, imagine switching on a light bulb now. The edge of the expanding sphere of light is the event horizon. For some reason, most people think of the particle horizon in space, i.e. the edge of the sphere now, and the event horizon in spacetime, but of course one can think of both in both ways.

What happens at the horizon, that is, in which direction objects cross it, whether they do so more than once, and so on depends on the cosmological parameters. Check out some explicit calculations for a wide range of cosmological models.

• As a prelude to the calculation paper, check out a nice paper on the classification of cosmological models. If you read just one paper on cosmology, this should be it. It contains a huge amount of information. It is not an exaggeration to say that other (quite well known) people have made entire papers out of one-sentence statements in this paper. I would even go so far as to say that actually grokking this paper is the closes thing to enlightenment a non-religious person can experience. :-)

4. Ishi Crew says:

Toby Ord has also written on ‘hypercomputation’ (beyond the Turing limit) as have others (some say its impossible, i’m agnostic—-it could be that just as Feynman pointed out quantum computing (and mechanics) is the norm in nature, so is hypercomputation but we just dont see it–the world looks classical and follows church-turing thesis.)

If hypercomputation could be realized in technology then maybe long distance travel is not an issue.

(There have been a couple recent papers by a group out of Oxford who claim the universe is not expanding–its not even a problem. Reminds me of Zwicky’s ‘tired light’ or related theories of static universes from 1930’s or before. I like these dissident theories, and similar others like hidden variable theories (stochastic electrodynamics), and ultrafinitism).

• John Baez says:

I don’t like “dissident” theories. I like correct theories, dissident or not: it’s hard enough just to be right. I think hypercomputation is very unlikely, but if some technologically advanced civilizations last for millions or billions of years they’ll have plenty of time to think about this.

• Reference, please, to such “Oxford papers”.

Probably not relevant here, but interesting: “Oxford” is not always the university.

• Ishi Crew says:

I ‘bookmarked’ the paper but i’d have to look it up—it was on arxiv and i may have misinterpreted it.

(it was also reported on media like phys.org–and other physicists said it was wrong–it was a different interpretation of astronomical data. it may have dealt with (nonexistance of) dark matter/energy. I interpreted it as similar to Mandelbrot’s view of Olber’s paradox (which i only read about on wikipedia though i did try to read some of mandelbrot’s books.) It was by a physicist (or group) affiliated with Oxford (or maybe Cambridge or some other UK university like UCL).

To me, there are different kinds of dissident or alternative theories—i might say heisenberg’s matrix mechanics , wave and bohmian mechanics are alternatives (or interpretations) –stochastic electrodynamics (eg Timothy Boyer) skirts the edge between alternative and ‘crackpot’. a ‘dissident’ could be an alternative or a crackpot.

My interest in these is somewhat like psychologists and educators who try to understand ‘abnormal psychology’ or why certain math problems which are thought to be ‘trivial’ some people just can’t seem to solve. I was and am one of these–its like you are ‘color blind’. (I also had synthesia and still do to an extent –so i see colors in symbols, hear sounds others dont hear, and see shapes others miss. This is why at times I can find people’s lost possessions –i found my in laws wedding ring she had been looking for for weeks–i thought it was a shiny piece of trash but showed it to her —i sometimes find flora and fauna people just walk by without noticing. )

• Maybe you are referring to some papers discussing the “tension” in the measurements of the Hubble constant. But no-one in that debate is claiming that the Universe is not expanding.

5. John Baez says:

Actually I thought galaxy clusters were gravitationally bound, in which case the Virgo Cluster, a much bigger assemblage than the Local Group, might hold together against the expansion of the Universe.

• John Baez says:

Toby Ord says galaxy clusters like the Virgo Cluster are gravitationally bound, but we now know the Local Group is not gravitationally bound to the Virgo Cluster: we are on our own.

6. Nick Nolan says:

Once you have seen one local group you have seen them all.

New, important stuff encountered when exploring the universe will probably decrease after you have explored the Local Group. There is this romantic notion of endless wonders in space but I seriously doubt it.

Maybe a special telescope and instrument calibration mission to cosmic voids is necessary, or some distant super-duper black hole or supernova remnant requires a special mission, but endless galaxy to galaxy exploration will probably yield less and less new and interesting stuff.

• John Baez says:

I was thinking of it more in terms of expanding civilization, not discovering new wonders. You can also argue that once a civilization has expanded to fill a whole galaxy, taking over other galaxies is a bit pointless. However, life forms have this habit of constantly wanting more—presumably because that’s the kind of life form that takes over.

7. John Baez says:

On the category theory community server someone pointed out this:

• Lawrence M. Krauss, Robert J. Scherrer The return of a static Universe and the end of cosmology.

Abstract. We demonstrate that as we extrapolate the current ΛCDM universe forward in time, all evidence of the Hubble expansion will disappear, so that observers in our “island universe” will be fundamentally incapable of determining the true nature of the universe, including the existence of the highly dominant vacuum energy, the existence of the CMB, and the primordial origin of light elements. With these pillars of the modern Big Bang gone, this epoch will mark the end of cosmology and the return of a static universe. In this sense, the coordinate system appropriate for future observers will perhaps fittingly resemble the static coordinate system in which the de Sitter universe was first presented.

8. How would such a civilization know if some explorers in some far corner of their currently accessible universe had (or) not expanded into regions which are no longer accessible? I find it more fascinating to think that intergalactic traveling civilizations, if they last so long, would inevitably lose part of their history.

• John Baez says:

How would such a civilization know if some explorers in some far corner of their currently accessible universe had (or) not expanded into regions which are no longer accessible?

They could not know for sure.

We can imagine a scenario like this:

We see a far-away galaxy and notice that its stars are arranged in artificial patterns that indicate an advanced technological civilization. But this galaxy is so far away that due to the accelerating expansion of the Universe we never see much of the future of this galaxy! We can wait for millions or billions of years, but it just gets red-shifted more and more, with its apparent time slowing down, until it dims to invisibility. So, we can only speculate about what this civilization will do.

9. Arun Singha says:

I must follow you. I love cosmology. Great 👌 Regards 🙏

10. Stan says:

The local cluster won’t get pulled apart because it is held in place by gravity? That’s not how the expansion of the universe works. Every point in space is becoming further away from every other point. The distance between your ears is expanding. Slowly. No force can overcome this. The local cluster will stay together longer because we are a local observer. To some distant observer on the other side of the universe right now, it will much more quickly vanish from the observable universe.

• John Baez says:

Stan wrote:

Every point in space is becoming further away from every other point. The distance between your ears is expanding. Slowly. No force can overcome this.

No, that’s not true. Well, people do say I’m getting a big head, and it’s probably true, but it’s not due to the expansion of the universe.

You can read a discussion of this issue here:

and there are references to sources that discuss it more deeply.

In a bound system, the expansion of the Universe does make the equilibrium position slightly larger than it would otherwise be, but at the scale of people’s heads, not to mention atoms, that is not measurable.

• Stan says:

It would have to, otherwise there would be missing energy input into the system to maintain the gap. Obviously this isn’t measurable unless you manage to live forever, something I definitely hope to do. Or at least long enough to visit mars. 👍

• John Baez says:

The expansion of the Universe makes the equilibrium position of my head slightly larger than it would be if the universe were not expanding – but it does not make my head keep getting bigger. If I died and were mummified, my head would not become twice as big in 10 billion years. It would stay exactly the same size (if not eaten by rats).

11. Gaynor Lowell says:

Don’t worry about it, enjoy your 3 score and 10. Stop sweating over the small stuff.

• John Baez says:

12. Seth E Whitley says:

You can use Markdown or HTML in your comments. You can also use LaTeX, like this: $E = m c^2$. The word ‘latex’ comes right after the first dollar sign, with a space after it.

13. Tudor Montescu says:

Enjoy it while the cost of long distance calls is decreasing. In 150 billion years it will get quite expensive

14. joel schlecht says:

I know you didn’t write the paper but I wanted to contest the notion of things being gravitationally bound. There really isn’t such a thing. There is gravitational equilibrium… Such as you standing on the earth. The gravitational force is in equilibrium with the force the ground pushes up on you do you don’t move. When the moon is overhead, it pulls on you and the ground pushes a little less so you weigh less but the whole system is still in equilibrium and you stay on the ground. But, if Jupiter came close enough…. It would suck you off the earth. Your not “bound” to the earth. If something were in orbit instead of on the ground… A small force would affect the distance.

The problem comes with potential/kinetic energy. As the cosmological constant increases the space between things.. it must exert a force because potential energy increases the further away things are and as the relative velocity increases, so does the kinetic energy. We don’t know where all this energy comes from, thus, dark energy but, energy is a force acting over a distance.

As the cosmological constant increases over time, the force exerted increases and so eventually it will be great enough to overcome our local cluster. It has already overcome super clusters that would have long ago been classified as ‘gravitationally bound” and we know they were because that’s how they clustered in the first place.

If the cosmological constant is allowed to increase forever… Eventually it will rip apart galaxies, star systems, planets, and even atoms.

• The cosmological constant does not increase over time. That’s why it’s the cosmological constant. Some people have come up with some ideas for types of “dark energy” (a really bad name; as Sean Carroll points out, everything has energy and many things are dark; sadly, his “smooth tension” never caught on) which do increase with time, leading to the “big rip” you described, but that is not the case with the traditional cosmological constant.

(Note that the Hubble constant is not called that because it is constant in time, but rather because it is the constant in an equation like $a$ is a constant in $y=ax+b$. That holds at any one time, but in general $H$ can change with time. Anyone who writes something like Hubble “constant” or calls it the Hubble “parameter” is showing a profound ignorance of the history of cosmology.)

• It’s fine to call it the Hubble parameter, but not because that should be used because the term Hubble constant is somehow wrong. In particular, using the term “parameter” for the Hubble constant as a function of time is close to the “not even wrong” category with regard to the history of cosmology.

• John Baez says:

The concept of “gravitationally bound” has a useful meaning for systems like galaxies, galactic clusters etc., though it’s true that a bound system can become unbound in a collision. For example, if another galaxy cluster whizzed past the Local Group, the galaxies in this group could cease to be bound. But this happens rarely enough that “gravitationally bound” is a sensible concept.

The problem comes with potential/kinetic energy. As the cosmological constant increases the space between things, it must exert a force because potential energy increases the further away things are and as the relative velocity increases, so does the kinetic energy.

That’s not how the cosmological constant works; you’re blending Newtonian physics and general relativity in an incorrect way.

Also: the cosmological constant does not increase with time. The density of dark energy might increase with time, and there are some very speculative theories where it does, but in plain old general relativity with cosmological constant, as used in the usual ΛCDM model of cosmology, the density of dark energy is constant.

15. Peter says:

This is all very nice to think about, but… We live here and now. Our action and especially inaction, is what counts and determines the future of “us”. I think AI will not come to rescue NS and thus in a not too distant future our thought revolve around other matter than how the universe will look like in a 1,000 years.

But again nice thought to relax during the inaction.

• John Baez says:

If you read this blog you’ll see that my serious articles concern how to fight global warming, and also how to get more mathematicians involved in practical problems. This article was “just for fun”—and it attracted about 100 times as many views.

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