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. sb tyroler says:

    First, I will qualify: I’m not a physicist, just interested. So go easy on me!

    When I read Krauss discussing the expansion of the universe, my understanding was that he was framing it in such a way as to say the “acceleration” of expansion would at a point in the future pass the threshold where the recession “velocity” of other galaxies in relation to our galaxy would redshift the wavelength as large as the visible universe and hence would disappear from our view. The implication to a lay-person is at that point the recession “velocity” exceeds the speed of light so that evidence if its existence would never reach us.

    So, my question: If you were going to explain to a lay audience that in a couple of trillion years, as a result of the expansion of the universe, the detection of other galaxies and the big bang would disappear from within our galaxy, how would you do it without using the misnomer “velocity exceeds the speed of light”?

  2. David C. says:

    James,
    I’m not going to be able to show you proofs, but we do know that Doppler shift definitely occurs with electromagnetic radiation as well as with sound.
    Two real-world examples are Doppler radar and police radar guns. Both involve beaming RF signals onto an object and measuring the reflection off of that object. The signal received is a higher or lower frequency than that emitted (that is, blue- or red-shifted) based on the velocity (relative to the radar gun) of the object that the signal reflected off of.
    So, while scientists may disagree over what specifically a large red-shift in a galaxy’s spectrum means, there is nothing implausible about it being a Doppler-like frequency shift.

    It’s also worth noting that motion isn’t the only thing that can cause a frequency shift. Gravity also does. This has also been demonstrated experimentally. When measuring a spectrum-shift of a large massive object like a galaxy, there will be some shifting due to gravity and some due to apparent velocity. I would assume that all the accepted mathematical models take both into account.

  3. Chris Mannering says:

    The expansion of the universe has an empirical speed of C. The Hubble Limit is 13.7B light years, give or take 300,000 years. So that means the universe has expanded at 2C across the observable diameter and C in any direction. Anything else, inflation, space-time expanding faster than light, any at all beyond what is observable, is theory, that isn’t confirmed. There’s no way that we can actually see an object that is at the time of seeing it, moving away from faster than light. Because if that was true then we would be able to see further than 13.7B years.
    Or is that wrong? Please do set me straight if it is. Many thanks.

  4. Kasuha says:

    This much is clear, I made exactly the same conclusion long time ago when I was thinking about what ‘expansion faster than speed of light’ actually means after hearing it somewhere.

    Related thing that confuses me to this day is the idea that dark energy is making the space expand, and if dark energy weren’t here, gravity would make the expansion stop and eventually collapse the universe back to single point.

    I have no idea where is that coming from. Space is not created when you pull two pieces of matter apart, and destroyed when you put them together again. I see no reason why gravity should have any effect on rate of universe expansion and no reason why there needs to be some kind of dark energy behind more space appearing in already existing space over time.

  5. PROFESSOR BLIMP says:

    so if the goodyear blimp falls into a wormhole, its nobodys fault but the blimps?

  6. Patrice Ayme says:

    I do agree with the article. However cogent the points, I don’t think they depict the whole story… Let’s call on more mathematics than usual in cosmology.
    A distance function can be defined within a Lorentzian manifold. If that distance augments at more than the speed of light, one can say so. One has defined, in some sense, a superluminal speed.

    One can also Riemannize spacetime, as is done in Quantum Field Theory, by changing the signature of the manifold from +++- to ++++. There again, and much more easily, one can talk about distance (especially as photons now can cover light years, instead of… zero).

    Now any smooth or analytic manifold can be embedded isometrically (respecting distance) in a space of dimension (n/2) (n+1), a (very famous) theorem of Nash. Then the universe is a submanifold of that larger Riemannian space. Then one can talk, literally, about the size of the universe. (It could be infinite.) In any case, one can talk about the change of size of the universe, and ponders if it is, or not, greater than the speed of light. (The mathematical subtlety is then to define the speed of light globally, although it’s only a local, even holonomic, that is, infinitesimal, at a point, notion)

    In any of the two cases, of the two sort of metrics constructed above the cosmological inflation posited in the usual Big Bang theory then occurs at “superluminal” speed. In practice, global light goes faster than local light.

    These ways of looking at expansion by using global metrics seem implicitly contained in the assertion of various cosmologists about superluminal speeds.

  7. mebigfatguy says:

    I love the youtubes and blogs by Sean. Each one i watch/read makes me feel a little dumber. At some point i’d expect to reach absolute dumbness, but haven’t so far. I look forward to that day.

  8. Why are causally disconnected parts of the CMB in apparent thermal equilibrium?

  9. John Merryman says:

    One of the main problems I have with the whole expanding universe idea is that it assumes one metric of space defined by the redshifted spectrum of intergalactic light and another by the speed of the very same light, against which to compare it.

    Basically that this light is redshifted because the source is moving away and thus as the light takes longer to cross, the spectrum is shifted, as a classic doppler effect. Yet that implicitly assumes a stable speed of light, since it is taking light longer to cross this space, so that there are more units, not expanded units.

    Remember Einstein said; “Space is what you measure with a ruler.” As one would assume the ruler for intergalactic light would be defined by the speed of light, if it is going to take light longer to cross over time, than what is defined by the redshift of the spectrum is not the same space as defined by the speed of the same light.

    Now the reason they say space itself is expanding and this isn’t just an expansion in space is because way back when, they discovered the galaxies appear to have little to no lateral motion to match the redshift and it increases directly proportional to distance, so this creates the impression that we are at the exact center of the universe. Then the theory became, that because “spacetime,” space itself is expanding and every point appears as the center.

    The obvious problem, or logically so, is that the very premise of “spacetime” is that light speed will remain Constant. Such that in an accelerated frame, both distance shrinks and time slows, so that the speed of light remains Constant. Yet if it is taking light longer to cross this distance between galaxies, in order to be redshifted, than it is not Constant to this space.

    It should be noted that we are in fact at the very center of our view of the universe and if redshift were actually an optical effect, like gravitational lensing, where the source is not affected, only the light traveling from it, than it would be quite logical that we would appear at the center of this effect.

    Although this would raise issues about how much we actually do understand about light, especially multi spectrum travel over vast distances.

  10. “Phillip Helbig, I am experiencing problems opening the links you have provided. Do you have the paper uploaded on arXiv or some other server?”

    Not sure why the links aren’t working; they seem to be OK. In any case, I wanted to put up the arXiv links to Lake’s paper and my paper on the flatness problem.

  11. “Why are causally disconnected parts of the CMB in apparent thermal equilibrium?”

    This is what is known as the isotropy or horizon problem. AFAIK, no-one has come up with a better explanation than inflation to solve it.

  12. Chris says:

    As a PhD student working on inflation I appreciate this post, but I must admit I’ve fallen into the trap of using this description of superluminal expansion on occasion. Particularly when trying to explain what I study to people without a scientific background, like my parents, who don’t want to listen to technobabble about units and just want to know if it’s faster than light or not. I could try and explain how expansion rates and speeds are not equatable objects and give a scientifically correct answer, at which point my listener would lose interest and respond with some kind of grunt of disapproval, or I could say “Yes, the expansion is faster than the speed of light! Isn’t it cool?”

    I know deep down I’m being misleading but it’s tough to remain rigourous when working to a very low level of understanding. I sometimes add some kind of statement to say it’s not technically true but you can think of it as being faster than light in a very loose sense, but this doesn’t help understanding, it’s just a disclaimer really.

    Either way I’d probably rather slightly mislead people but instill some kind of interest in cosmology, than dive into the scientifically correct explanation and make people think the subject is boring. If that makes me a bad scientist then so be it. Though if I ever slip up and say this in a paper or anything then I acknowledge and await bmy impending crucifixion!

  13. eric says:

    In particular, there’s no reason whatsoever that this apparent velocity can’t be greater than the speed of light.

    This has always been how I naturally and normally interpreted the claims you’re railing against. Maybe I’m unusual in that way (I doubt it), but because I’ve generally interpreted the phrasing you obect to as meaning the alternate phrasing you prefer, I do see this as not much more than an ‘explaining technical terms in natural language’ issue.

  14. Peter Ozzie Jones says:

    Alan Guth, in a 2 minute video clip here:
    http://nautil.us/blog/the-father-of-inflation-clears-up-a-big-misunderstanding

    seems to make it clear what is meant by the expansion of this part of the universe?
    What do you think?

  15. redmudislander says:

    Reading the article made me think of the entire history of expansion at a glance.
    I began by seeing in my mind the familiar horizontal bell shaped expansion diagram with the inflation era on the left, and the present era on the right.
    Then I began to ponder the primordial ball on the left, 13.7 billion years ago.
    Let’s suspend time and think of the ball.
    We know that it was unimaginably hot and dense.
    We know that it was about to begin expanding at some unfathomable rate.
    Among the things we don’t know are how big it was,
    and (now that it has expanded and cooled) what percentage of it is the sphere we now call our Cosmological Microwave Background.
    I find it interesting to learn that we know our velocity inside that sphere though,
    and fascinating to know that we can graph the shape of the history of the Hubble constant to extreme extrapolations on the left, and make interesting prognostications about the shape on the right.
    Regards.

  16. redmudislander says:

    Here’s an off topic –
    Since the Higgs field has a non-zero potential, could it be described as having a ‘temperature’ like the CMB does? If so, then might it diminish too?

  17. arch1 says:

    Is it still possible that our universe is finite in spatial extent? If yes, and our universe *is* in fact finite, wouldn’t it have a well defined size at each point in time? If again yes, why wouldn’t it useful to refer to the rate of change of that size as “the expansion rate of the universe”?

  18. Is it still possible that our universe is finite in spatial extent?

    Yes.

    If yes, and our universe *is* in fact finite, wouldn’t it have a well defined size at each point in time?

    Yes.

    If again yes, why wouldn’t it useful to refer to the rate of change of that size as “the expansion rate of the universe”?

    Useful for what? As I mentioned above, even if the rate of change of the scale factor is dubbed “the expansion rate of the universe” and even if this is less than the speed of light, it is still possible for the change in proper distance with time (these are the distance and speed in the law v=HD) to be greater than the speed of light, so in the discussion in this thread it is probably not useful. Possible? Sure.

  19. John Merryman says:

    red,

    “Since the Higgs field has a non-zero potential, could it be described as having a ‘temperature’ like the CMB does? If so, then might it diminish too?”

    You might consider the vacuum fluctuation as a thermal effect as well and that presumably would not diminish.

    One of the ideas I try bringing up is that if we think of time, not as the point of the present moving from past to future, which physics codifies as measures of duration, but the changing configuration of what is, such that the future becomes past, as in tomorrow becomes yesterday because the earth turns, then time is more an effect of activity, similar to temperature and what we measure is essentially just frequency. Given that temperature is a mass effect of frequency and amplitude, this would make temperature a more comprehensive effect than time.

    Obviously it hasn’t been a popular idea to raise, but consider that duration is really just the state of the present, as events form and dissolve. As well as explaining determinism, in that events have to occur, in order to be determined. They are first in the present, then in the past. Also that the conservation of energy means it only exists as the present, not falling into the past, or rising in the future. Though by going from one event to the next, creates the effect of time.

    It is just that our sense of perception is flashes of cognition, so we think of it as a point of the present moving along the narrative timeline, but then we still see the sun rising in the east and setting in the west.

  20. Hi Sean,
    1) Can’t the expansion of the universe can’t be measured by the decrease of the net density of the universe? So couldn’t its units be kg/(m^3)/second ?

    2) If someone hypothetically shines a flashlight at the edge of the universe, would the light keep shining in the same direction because the universe is “out-expanding” it, or would it curve back on itself as a person would do if he walked in a straight line on Earth?

  21. Richard E says:

    I agree that “superluminal” is a silly appellation for inflation, but in any FRW universe (where you do have a well defined slicing) the spatial distance to points in the universe beyond the current horizon will increase their distance from us by more than $c \Delta t$ in a time $\Delta t$…

  22. Chris Mannering says:

    Re my earlier post. I don’t know why but I read Sean Carol’s header as “The universe [CAN] expand faster than the speed of light”. So all I said was another way of saying what he said. Sorry about that (it’s unlikely anyone much read my comment anyhow, but just sayin’)

  23. Chris Mannering says:

    The speed of light is actually the maximum rate of expansion, where the vast majority of expansion between two arbitrary points is much less than C. It’s only C between the ‘centre’ of any light cone, and the outer edge of that light cone. All shorter distances within that stretch on those terms, are obviously less than C.

  24. Chris Mannering says:

    Inflation is a terrible explanation because we’re still left with ‘how did all that internal structure exist at t=0 that the ordered universe came out of it”. Inflation can never explain that, and so for that reason Inflation only works in the case there is a vast multiverse in which every possible kind of universe exists and so even unbelievably unlikely ones like ours must too.
    Come on, that’s not an explanation. That’s quitting.

  25. David C. says:

    @Chris Mannering: What you wrote regarding C is one of the fundamental misunderstandings of general relativity.

    There’s nothing that says two arbitrary points can’t recede from each other at a speed faster than C. It only says that if these two points pass each other, an observer at one point won’t be able to observe the other passing at a speed faster than C. Some distant observer, however, can observe each point moving at some large percentage of C in opposite directions, add the vectors and conclude that they are approaching each other at a velocity faster than C.

    And why does all this seeming contradiction work? Because the three objects (the two points in motion and you, the observer) are all in different frames of reference – a situation beyond the scope of GR’s predictions. It’s only when two objects are in the same frame (e.g. when two points pass each other and one is observing the other) that GR’s predictions are applicable.

    Your talk of light cones only describes what we can observe. It doesn’t say anything about what may or may not exist beyond that – only that it can’t be observed.