# The Universe Never Expands Faster Than the Speed of Light

Breaking my radio silence here to get a little nitpick off my chest: the claim that during inflation, the universe “expanded faster than the speed of light.” It’s extraordinarily common, if utterly and hopelessly incorrect. (I just noticed it in this otherwise generally excellent post by Fraser Cain.) A Google search for “inflation superluminal expansion” reveals over 100,000 hits, although happily a few of the first ones are brave attempts to squelch the misconception. I can recommend this nice article by Tamara Davis and Charlie Lineweaver, which tries to address this and several other cosmological misconceptions.

This isn’t, by the way, one of those misconceptions that rattles around the popular-explanation sphere, while experts sit back silently and roll their eyes. Experts get this one wrong all the time. “Inflation was a period of superluminal expansion” is repeated, for example, in these texts by by Tai-Peng Cheng, by Joel Primack, and by Lawrence Krauss, all of whom should certainly know better.

The great thing about the superluminal-expansion misconception is that it’s actually a mangle of several different problems, which sadly don’t cancel out to give you the right answer.

1.The expansion of the universe doesn’t have a “speed.” Really the discussion should begin and end right there. Comparing the expansion rate of the universe to the speed of light is like comparing the height of a building to your weight. You’re not doing good scientific explanation; you’ve had too much to drink and should just go home.The expansion of the universe is quantified by the Hubble constant, which is typically quoted in crazy units of kilometers per second per megaparsec. That’s (distance divided by time) divided by distance, or simply 1/time. Speed, meanwhile, is measured in distance/time. Not the same units! Comparing the two concepts is crazy.

Admittedly, you can construct a quantity with units of velocity from the Hubble constant, using Hubble’s law, v = Hd (the apparent velocity of a galaxy is given by the Hubble constant times its distance). Individual galaxies are indeed associated with recession velocities. But different galaxies, manifestly, have different velocities. The idea of even talking about “the expansion velocity of the universe” is bizarre and never should have been entertained in the first place.

2. There is no well-defined notion of “the velocity of distant objects” in general relativity. There is a rule, valid both in special relativity and general relativity, that says two objects cannot pass by each other with relative velocities faster than the speed of light. In special relativity, where spacetime is a fixed, flat, Minkowskian geometry, we can pick a global reference frame and extend that rule to distant objects. In general relativity, we just can’t. There is simply no such thing as the “velocity” between two objects that aren’t located in the same place. If you tried to measure such a velocity, you would have to parallel transport the motion of one object to the location of the other one, and your answer would completely depend on the path that you took to do that. So there can’t be any rule that says that velocity can’t be greater than the speed of light. Period, full stop, end of story.

Except it’s not quite the end of the story, since under certain special circumstances it’s possible to define quantities that are kind-of sort-of like a velocity between distant objects. Cosmology, where we model the universe as having a preferred reference frame defined by the matter filling space, is one such circumstance. When galaxies are not too far away, we can measure their cosmological redshifts, pretend that it’s a Doppler shift, and work backwards to define an “apparent velocity.” Good for you, cosmologists! But that number you’ve defined shouldn’t be confused with the actual relative velocity between two objects passing by each other. In particular, there’s no reason whatsoever that this apparent velocity can’t be greater than the speed of light.

Sometimes this idea is mangled into something like “the rule against superluminal velocities doesn’t refer to the expansion of space.” A good try, certainly well-intentioned, but the problem is deeper than that. The rule against superluminal velocities only refers to relative velocities between two objects passing right by each other.

3. There is nothing special about the expansion rate during inflation. If you want to stubbornly insist on treating the cosmological apparent velocity as a real velocity, just so you can then go and confuse people by saying that sometimes that velocity can be greater than the speed of light, I can’t stop you. But it can be — and is! — greater than the speed of light at any time in the history of the universe, not just during inflation. There are galaxies sufficiently distant that their apparent recession velocities today are greater than the speed of light. To give people the impression that what’s special about inflation is that the universe is expanding faster than light is a crime against comprehension and good taste.

What’s special about inflation is that the universe is accelerating. During inflation (as well as today, since dark energy has taken over), the scale factor, which characterizes the relative distance between comoving points in space, is increasing faster and faster, rather than increasing but at a gradually diminishing rate. As a result, if you looked at one particular galaxy over time, its apparent recession velocity would be increasing. That’s a big deal, with all sorts of interesting and important cosmological ramifications. And it’s not that hard to explain.

But it’s not superluminal expansion. If you’re sitting at a stoplight in your Tesla, kick it into insane mode, and accelerate to 60 mph in 3.5 seconds, you won’t get a ticket for speeding, as long as the speed limit itself is 60 mph or greater. You can still get a ticket — there’s such a thing as reckless driving, after all — but if you’re hauled before the traffic judge on a count of speeding, you should be able to get off scot-free.

Many “misconceptions” in physics stem from an honest attempt to explain technical concepts in natural language, and I try to be very forgiving about those. This one, I believe, isn’t like that; it’s just wrongity-wrong wrong. The only good quality of the phrase “inflation is a period of superluminal expansion” is that it’s short. It conveys the illusion of understanding, but that can be just as bad as straightforward misunderstanding. Every time it is repeated, people’s appreciation of how the universe works gets a little bit worse. We should be able to do better.

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### 140 Responses to The Universe Never Expands Faster Than the Speed of Light

1. Steve Ruis says:

These discussions always suggest to me that there is something I am missing. That fact is the relationship between the material universe and “space.”

Was space there when the Big Bang occurred or was it created by the Big Bang? Now I know that one cannot define “space” without referring to material things in it, but if space were allowed a creation separate from the matter distributed in it, we would have some interesting possibilities. Like the universe could appear to be expanding faster over time, if space were expanding at a slower rate than it had formerly, leaving the matter in it appearing to be traveling faster. Hey it isn’t any weirder than dark matter and dark energy!

This is all quite beyond me, but fascinating nonetheless. BTW I especially enjoyed your comment on another comment about the joy of speculating.

2. Amrit Sorli says:

Universe do not expand at all.

3. James Collins says:

In the latest mini-course at World Science U, Prof Steinhardt seemed to entirely demolish “Inflation Theory” in its various forms. His arguments certainly seemed convincing –as Alan Guth’s arguments previously had also been convincing. This almost-mathless layman has no way of deciding. So, I’m going to go with whatever Sean Carroll says. Is IT dead? or still viable?

4. Tim Maudlin says:

This is very helpful, Sean: excellent!

I have been thinking about the term “the expansion of space”, especially as it is used in supposedly physical explanations such as: “the CMB is so cold because the expansion of space since it was emitted has increased the wavelength”. I think this also makes little physical sense since the most common definitions of the “expansion of space” are co-ordinate dependent, and co-ordinates don’t have physical effects. But two quick questions:

1) you say that “there’s no reason whatsoever that this apparent velocity can’t be greater than the speed of light”. If I use the Relativistic Doppler shift formula, then there is a reason, yes? Why would anyone use the classical formula?

2) Define the “Doppler portion” of an observed spectral shift this way: parallel transport the 4-vector of the emitter along the path of the photon itself to the absorber, and calculate the Relativistic Doppler effect from comparing those. Question: will this always account for the entire observed spectral shift or not? (I have not been able to get agreement about this from my sources.) If so, then one could in a reasonable sense say that all spectral shifts are pure Doppler (in this sense), so “the expansion of space” plays no role.

5. Sean Carroll says:

James– Inflation is completely alive and viable. It has problems, as it always has had, and it’s a good thing that cosmologists (including me) are increasingly taking those problems seriously rather than papering over them. But it’s still the best idea we have about the very early universe.

6. Andy Vivas says:

Thank you so much for clarifying this for us Professor. As always your communication style is elucidating.

Andy

7. Alexander Yosifov says:

@James Collins, considering the latest Planck satellite data we can seriously start questioning the very nature of the inflationary paradigm. Now days inflation seems less likely than ever.

8. Sean Carroll says:

Tim– I can’t think about this too carefully now because I am supposed to be finishing my book! But the fundamental issue relevant to this post is that the application of any Doppler formula won’t make sense when galaxies are so far away that light from them hasn’t gotten to you in the whole history of the universe. (I.e. they are outside the particle horizon.) You can still define a velocity by calculating the time derivative of the physical distance along comoving slices, but you’ll easily get an answer that is greater than the speed of light, and you should probably just resist the temptation.

9. Alexander Yosifov says:

Sean, isn’t the only reason inflation is still alive simply the fact it is so easily adjustable to fit almost all data? Planck2013 ruled out a big fraction of the models, including chaotic inflation which was the most promising one to explain the low entropy state of the early universe. It seems like a matter of time before other, more precise measurements, rule out the rest of the models.

10. Tim Maudlin says:

OK, I see. I thought you meant using an observed shift to do the calculation, but I see what you have in mind.

Thank you very much, Sean, the post is very enlightening and specially after your suggestion about reading Tamara Davis and Charlie Lineweaver article found in Arxiv. It is something I’ve always asked to myself. It is the expansion universe’s scale , everything is stuck in the fabric of the universe and the space-time expands. This is my growing understanding of this (may be wrong) but amazing though.

12. Go Cubs says:

This was perhaps the most intelligent blog post you’ve ever done in terms of pedagogy because I kept hearing the same thing about how space can expand faster than light and the true explanation is not that difficult to understand. Well done. The clarity involves a little math in seeing that velocity is not the same as velocity over distance and understanding what is being measured by the units.

13. David C. says:

I’ll start by admitting that my scientific knowledge on these subjects is at the level of hand-waving analogies that you see on Discovery Channel programs, so please forgive me if what I’m about to write makes absolutely no sense.

It would seem to me that the very concept of the universe expanding with any particular velocity is meaningless. As you wrote in “Does Space Expand?”, we are not actually observing the expansion of space, but are trying to find a reasonable explanation for why (apparently) distant objects have a red-shift that seems to indicate that they’re moving away from us at high speed.

I’ve heard the rubber-sheet theory (as, I’m sure, has everybody else), and I agree that the analogy only goes so far, but it seems useful at a hand-waving non-mathematical explanation.

Where I’ve got a problem is that it would seem that in order to define the “velocity” of this expansion, you would somehow need to be able to detect the edge of the universe, and more specifically, opposite edges (and by implication, have a concept of a “center”), and then measure these opposite edges receding from each other. Sort of like what you could do if you were inside a rubber balloon that was being inflated.

But of course, this doesn’t seem possible. At least not by any technology that currently exists. We can’t “see” the edge of the universe. There is a maximum distance that we can see with radio astronomy, but it seems logical that the universe may be even larger and that we simply have no ability to see farther. And if you can’t see the edges, then you can’t define a center either – we are always living in the center of what we can observe, but that doesn’t seem like a useful piece of information here.

And this ignores the idea that we may not be able to detect the edge even if we could see that far. If the universe is a closed system that we’re inside, then is it even theoretically possible to detect the edge? It’s like that (again, imperfect) analogy of walking on the surface of a sphere, like the Earth. You can’t detect the “edge” because your entire domain is the surface, which is curved and folds onto itself. So (if this can be analogized to an extra dimension or two) it would seem that if we could somehow view into infinite distance, we wouldn’t see an edge, but we’d ultimately “wrap” along some curve and see ourself (or something we “know” to be in a different direction.) Maybe we could measure the distance for a round-trip and apply some math to determine the size of the universe (much like how knowing the size of a sphere’s longitude can be used to compute its radius and volume), but it’s unlikely we’ll ever have the technology to even attempt such an experiment, even if it should be theoretically possible.

So we’re back to asking what the velocity of expansion could possibly mean, since we really can’t compute the current size, let alone observe how it changes over time.

I’m sure the cosmologists (and you) have something in mind when talking about the concept of an expanding universe, but nothing I’ve heard goes beyond simplistic analogies that, as you’ve written, break down if you look too closely.

I’m sure I’m missing some critical facts here, but I’m hoping that maybe it is possible to hear an explanation that makes sense without massive amounts of math that I’d need to complete a PhD program to understand.

14. trivialknot says:

Davis and Lineweaver also wrote an article for Scientific American. I read it when I was in high school and it made me so angry. Everything I’ve been told is a lie! I had trouble explaining this to my classmates though.

15. Shmi Nux says:

Isn’t there a Youtube video somewhere of a balloon being inflated, and an ant, representing light, crawling toward some mark on the balloon? And how the ant can always reach that mark eventually, no matter how fast the balloon is inflating, as long as the inflation rate, measured as the relative rate of change in the balloon radius over time, is not increasing?

If not, someone should make one. If yes, maybe someone can link it.

16. Steve Ando says:

@Alexander Yosifov
If the Planck results are so bad for inflation, if inflation is in serious trouble then
why did the Planck team write this at the end of the
-Planck 2015 results. XIII. Cosmological parameters- paper?
“The Planck results offer powerful evidence in favour of simple inflationary models,
which provide an attractive mechanism for generating the
slightly tilted spectrum of (nearly) Gaussian adiabatic perturbations
that match our data to such high precision. ”
This comes from the Planck team and not from Alan Guth, not from Andrei Linde.

17. José Roberto de Siqueira Filgo says:

Dear Mr Carroll,
I loved your explanation! For the first time I red a clear explanation about, in very simple and accesible language.
I finnaly understood the concept wich is not very clear in many experts popular explanations. Congrats

18. “Inflation is completely alive and viable. It has problems, as it always has had, and it’s a good thing that cosmologists (including me) are increasingly taking those problems seriously rather than papering over them. But it’s still the best idea we have about the very early universe.”

I agree completely here. However, I would disagree with: ” So, I’m going to go with whatever Sean Carroll says.” Not because of any criticism of Sean, far from it, but because scientific opinions shouldn’t be based on popularity, or visibility (like writing a blog).

19. “considering the latest Planck satellite data we can seriously start questioning the very nature of the inflationary paradigm. Now days inflation seems less likely than ever.”

Why?

20. “isn’t the only reason inflation is still alive simply the fact it is so easily adjustable to fit almost all data? Planck2013 ruled out a big fraction of the models, including chaotic inflation which was the most promising one to explain the low entropy state of the early universe. It seems like a matter of time before other, more precise measurements, rule out the rest of the models.”

Invalid extrapolation. People used to plot the Hubble constant as a function of time—the time of publication of the corresponding papers. Extrapolation predicted that it would reach zero in the year 2005 or whatever. In general, science progresses by ruling out hypotheses, but this does not mean that if one waits long enough then all hypotheses will be ruled out.

21. Lee Loveridge says:

Hmm, I think the suggestion of superluminal expansion during inflation might be used to help explain that during an inflationary epoch (including now) objects at the edge of observable move out of the observable as if they had been pushed faster than the speed of light. The number of objects which are observable becomes smaller and smaller. While during non-inflationary epochs objects that are just barely unobservable become observable as if they were traveling just under the speed of light.

I agree it is a flawed explanation. It is in fact a matter of the acceleration. During inflation apparently subluminal velocities turn into apparently superluminal ones. During non inflation, apparently superluminal turn into apparently subluminal ones. Still in this sense it might fall into the realm of trying to explain technical ideas with less precise language.

22. Mogens Michaelsen says:

If you imagine a universe with infinite space that are slowly expanding, it is easy to see, that no matter how low the expansion rate is, there will always be objects so far away from you, that the distance increases more than 1 light-year in a year!

Clearly this doesn’t mean that the object is moving away from you with more than the speed of light. But as far as I can see, it nevertheless has the consequence, that you are not able to see the object, just AS IF it moved away with superluminal speed?

I feel a little better about getting this wrong when two of the first incorrect explanations in Appendix B of the Davis and Lineweaver paper are from Feynman and Weinberg. I’ll need to give the arxiv article a more thorough read when I get a chance.

Also, “Lineweaver” is a terrifically appropriate surname for someone explaining consequences of General Relativity.

24. Per says:

Hi,

What happens if you embed our expanding universe in a higher-dimensional flat space like R^5 or R^6, or whatever. Then you can define a velocity with respect to the coordinate axis of that larger space. Doing that, what is the acceleration rate then?

Thanks, Per

25. ” Then you can define a velocity with respect to the coordinate axis of that larger space.”

You can do it, but it is not very useful. Go back to the balloon analogy with a spatially closed universe. You can then ask what is the velocity of expansion of the balloon relative to its centre. This is a well defined concept. However, even if this is less than the speed of light, the relative velocities (in the sense of the velocity-distance law) can still be greater than the speed of light.

Folks interested in this should read Edward Harrison’s Cosmology: The Science of the Universe textbook.