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. “Clearly this doesn’t mean that the object is moving away from you with more than the speed of light. “

    Why not?

    Again, read Harrison, read Davis and Lineweaver.

  2. “Clearly this doesn’t mean that the object is moving away from you with more than the speed of light. “

    Why not?

    Again, read Harrison, read Davis and Lineweaver.

    .

  3. Daniel says:

    > The expansion of the universe is quantified by the Hubble constant, which is typically quoted in crazy units of kilometers per second per megaparsec.

    These units look very natural to me. Kilometers per second is a velocity. The Hubble constant is the velocity at which any two points a megaparsec apart are receding from one another, corresponding to the redshift of light emitted at one of them and observed at the other at that moment. Is that right?

    Of course this isn’t a real, local, relative velocity, as you point out, and it can be greater than the speed of light.

  4. “There are galaxies sufficiently distant that their apparent recession velocities today are greater than the speed of light.”

    I think I understand the point, but then I’m wondering about the consequences of this. If two things are close together and have an approach velocity, then the complicating factor of the expansion of the space “underneath” them isn’t interesting because they’re close. But in the case of two things very distant from each other, is it interesting to look at their velocity in space compared to each other as different from the expansion of space beneath their feet? These are two different factors, right?

  5. “The Hubble constant is the velocity at which any two points a megaparsec apart are receding from one another,”

    Right. But the distance is the proper distance and the velocity is the change in proper distance with time. These are not quantities which are directly observable. This is pure kinematics; no physics, certainly no GR needed. If the universe is homogeneous and isotropic, then velocity must be proportional to distance, otherwise it will not always be homogeneous and isotropic.

    ” corresponding to the redshift of light emitted at one of them and observed at the other at that moment. Is that right?”

    No, if by “corresponding to the redshift” you mean somehow calculating the velocity from the redshift. You just can’t do that in cosmology without additional assumptions or in the limit of very small redshifts.

    “Of course this isn’t a real, local, relative velocity, as you point out, and it can be greater than the speed of light.”

    It is real, it is relative, but it is not local in the sense that it is not a velocity of objects passing one another.

    Read Harrison’s paper on this topic.

  6. trivialknot says:

    @Mogens Michaelsen
    Using the recessional velocity v = Hd, some galaxies may be receding faster than light, and yet still be observable. As @Shmi Nux mentioned above, you can mathematically analogize it to an ant crawling along a balloon as it stretches. Even if the ant’s starting point is receding faster than ant’s crawl speed, the ant will still eventually get to its destination.

    Of course, this assumes that the radius of the balloon expands at a constant rate, while inflation is more analogous to a radius that expands at an exponential rate.

  7. Sharan says:

    Thank you, that was very informative. I am taking a course on GR and I was confused about relative velocity in GR. I can see why you say notion of velocity doesn’t make sense over long distances. But when we measure the “velocity” of far away galaxies what is it that we measure? Is it not the covariant derivative of the 4-position vector? Or do we consider the space time to be near Minkowski in long ranges as long as we don’t go too close to the Big Bang?

    Thanks,
    Sharan

  8. BobC says:

    The snarky side of my brain made me type the following:

    “Of *course* inflationary expansion never exceeded the speed of light! That’s because both time and space also stretched, keeping the speed of light constant (or nearly so).”

    Then my brain broke thinking about what time would then be like, pre-inflation.

  9. The Drinker says:

    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.

    Wait, I thought special relativity did away with the idea of a global reference frame and made all reference frames relative and subjective.

  10. Reading this prompts my PoV on our accelerating universe and decoupling Mass from matter in a the permanently warped fabric of spacetime (the second manuscript is far more substantive on hard math and clarifying assumptions).

  11. marten says:

    Nothing can go faster than the speed of light ceteris paribus.

  12. Alexander Yosifov says:

    Steve, the Planck Collaboration does favor the simple inflationary models over the more complex ones, in fact, it ruled most of them. However, the data shows the simple models which can account for the observed near-Gaussian perturbations suffer from what is referred to as the ‘unlikeliness problem.’ Random initial conditions do not lead to inflation. The inflaton field must satisfy specific properties in order for inflation to be triggered. As I mentioned it earlier, inflation is still around only because the mathematical model is easily adjustable and by manipulating parameters here and there one can make it account for almost all data. Furthermore, the universe seems to be incredibly simple, simplicity which could have been set very early on.

  13. Alexander Yosifov says:

    Steve Ando, the Planck Collaboration does in fact provide support for the simple inflationary models over the more complex ones, which rules out completely. However, the simple inflationary models which explain the near-Gaussian perturbations suffer from what is referred to as the ‘unlikeliness problem.’ Hence, random initial conditions do not lead to inflation. In order for an exponential entropy increase to be initiated specific initial conditions have to be satisfied. On the other hand, the most favorable model for explaining the low initial entropy of the universe is chaotic inflation, which is now ruled out. The other reason regarding this particular issue points to the multiverse. Therefore it is safe to say inflation needs to be replaced. The reason why inflation is still on is simply because it is very easily adjustable. Altering parameters here and there makes different models which cover all possible observations.

  14. Alexander Yosifov says:

    I apologize for the two posts, internet issues.

  15. Dick Atkinson says:

    I thought the whole point of the inflation theory was to solve the horizon problem by outpacing lightspeed?

  16. Antonio (AKA "Un físico") says:

    Nowadays, in our present universe: “objects beyond the Hubble sphere recede faster than the speed of light”. If anyone wants to know more about this sentence, please visit my document at: drive.google.com/file/d/0B4r_7eooq1u2OHBKOFN6dEdHRWc/edit ; please, watch & understand diagram 9 (pg. 27).

  17. Bee says:

    You don’t even need an expanding background to find ‘something’ that seems to be moving faster than light, see eg http://backreaction.blogspot.com/2015/04/photonic-booms-how-images-can-move.html

  18. Jshobe says:

    Thank you, Sean. Very enlightening and confirming. I think of the expansion of the universe as into nothing – a place where there are no speed limits.

  19. Peter B. says:

    How about inflation right after the big bang? I know that it makes no difference how big the universe is, but: in that case the rate of inflation does matter, it had to be sufficiently high for us to see the CMBR today. And the same applies to gravitational waves. How would you explain the rate of inflation in this case, it was higher/faster than… what?
    Or from the other way around: how fast did the rate of inflation have to be after the big bang to result in a universe that has these imprints like the CMBR and gravitational waves?
    I am asking this because so far it was this context where I heard about “space expanding faster than the speed of light” the most.

  20. “I thought the whole point of the inflation theory was to solve the horizon problem by outpacing lightspeed?”

    Depends on what you mean by “point”. Guth was trying to solve the monopole problem, and noticed that it would solve the flatness and isotropy (horizon) problems as well. Whether the monopole problem is really a problem is not clear; certainly the theories which predicted monopoles have been ruled out on other grounds (non-observed proton decay, for example). The isotropy problem does seem difficult to solve without inflation. Yes, it does have to do with superluminal expansion. However, Sean’s point was that it is wrong to equate inflation with superluminal expansion and the lack of inflation with the lack of superluminal inflation. (As for the flatness problem, I, along with Kayll Lake, am in a minority who claims that it is not really a problem, or at least not correctly understood. See his paper and my paper on this topic. A first step is to realize that the flatness and horizon problems are qualitatively quite different: the latter asks the question why the universe is homogeneous and isotropic and wants an answer other than “initial conditions” (which ties in to one of the few good criticisms of inflation: if it works only with special initial conditions, it is not very attractive as an explanation for avoiding other special initial conditions) while the former exists even assuming a completely homogeneous and isotropic model. In other words, the horizon problem asks why the universe is described by a Friedmann-Lemaitre model and the flatness problem is concerned with how likely the observed parameters of this model are.

    Feel free to refute my paper, but at least try to refute Lake’s as well.

  21. Alexander Yosifov says:

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

  22. Fred E Duncan III says:

    The speed of light & all what we call the laws of physics are continually changing, proved by the fact that trying to get the two fields of physics to mesh wont work, & also the law of observing messes with the results. The universe is expanding which means that everything in it is expanding. This isn’t noticeable because everything stays the same size in relation to everything else. This also means that the laws we think are fixed, are not. the speed of light is stretching along with everything else, but we will not be able to measure this effect unless we could step outside of our universe to be outside the field of effect. Simple common sense.

  23. David C. says:

    BobC wrote:
    Of *course* inflationary expansion never exceeded the speed of light! That’s because both time and space also stretched, keeping the speed of light constant (or nearly so).

    I have thought something along those lines for a long time and it makes perfect sense to me. I’m sure it can’t be right, because if it was, experts in the field wouldn’t be talking about superluminal expansion, but I haven’t run across anything that explains why it is incorrect (or at least not preferred by cosmologists.)

    Actually, if I think about it, if you assume that space-time itself is expanding, then I would think that you couldn’t possibly be aware of it because all your bases for measurement would also be expanding. The apparent rate of expansion would be zero to anybody inside the universe (and it’s doubtful we would ever be able to take a measurement from outside!)

    Of course, if expansion was as described above, and we therefore can’t detect it, then we’d have to find some other explanation for why distant galaxies appear to be receding from us at rates that correlate to distance.

  24. Jesse M. says:

    Part of the root of the problem with defining velocities of distant objects is the “relativity of simultaneity”–in relativity different coordinate systems can disagree about whether two events at distant locations happened simultaneously (at the same time-coordinate) or not, and all these coordinate systems are equally valid as far as the laws of physics are concerned. Once you have chosen a simultaneity convention, and divided 4D spacetime into a stack of 3D “simultaneity surfaces”–what is known as a ‘foliation’ of the 4D spacetime–then there is a pretty natural way to define how fast distant objects are moving away from you, relative to that foliation. Between any two simultaneity surfaces, you can define the time between them as measured by you in terms of the time that elapses on your own clock between them, and the distance between you and another object on each simultaneity surface can be defined in terms of the “proper distance” along the shortest space-like path between the two of you that lies on that surface (the proper distance can be understood in terms of having a series of short rulers moving inertially, whose ends all touch “simultaneously” according to your chosen simultaneity convention, and then you just add up the distance along all these rulers to get the proper distance along the path they lie along at that moment). Then the average speed of the object relative to you between the two simultaneity surfaces can be defined as the change in its proper distance from the first simultaneity surface to the second, divided by the proper time you measure between the two surfaces.

    It’s this type of relative velocity that cosmologists are usually referring to when they talk about the speed that galaxies are receding from us (they are making use of the most ‘natural’ simultaneity convention in the context of cosmology, the one that makes it so that the density of matter/energy throughout the universe is approximately uniform at any given moment), and this velocity can be arbitrarily large. But as Sean said, it’s fundamentally different from the local relative velocity of an object passing right next to you, which can be measured in your own local inertial rest frame (with the speed of light limit only applying to inertial frames, even in special relativity where spacetime isn’t curved).

  25. James Marlow says:

    Hello,
    After watching and reading many different and lovable, except Leonard Susskind (what the hell is with the hologram nonsense), physicists I’ve come to think there are just as many opinions as to the nature and grand makeup of the Universe as these fine physicists. Notice I didn’t say ‘Design’ as there is no design-it’s totally random: nothing and nobody is that connected and that smart. Nature itself puts on this grand show and it has been quite a show indeed. I always took Alan Guth’s assertion of cosmic inflation as meh, but like others have nothing else to put in its place, yet. But I still think good, kind Alan has been bouncing around in his office a bit too long and I am a Big Bang heretic. Perhaps the concept of gigantic spatial membranes sloshing about in the nothingness is more to my liking and these brane universes collide in several locations up, down, length and breadth every few hundred trillion years. BUT WE DON’T KNOW, do we. As to the speed of light, we either have it or we don’t, personally I think there is a caveat as yet undiscovered. And really folks, Professor Einstein didn’t give us much of a notion what type of “fabric” space is that make it so cohesive. If there is “something” that space is made of then there will be drag on particles or spaceships and planets moving through it. That something however small will eventually force an object to slow down and stop-if it was moving in a straight line. But like regenerative brakes that slowing puts energy back into the universe (EMPTY SPACE).
    Oh, one other thing. As a non scientist and outsider, I do know that Hubble or his heirs used the concept of Doppler Shift when describing the red shift of objects and believing them to be moving away. My early studies taught me that the Doppler Shift was for sound pressure waves in an atmospheric medium, clearly not the same use as that described by Hubble and friends. Can anyone enlighten me here? Thanks