Is energy conserved in a Universe with dark energy? (Synopsis)

“If you put yourself in a position where you have to stretch outside your comfort zone, then you are forced to expand your consciousness.” -Les Brown

On the one hand, you’ve got gravitation, the most powerful force in the Universe, trying to attract all the matter in it together. If it had its way, not only would everything eventually merge together, but the Universe itself would recollapse!

Image credit: Eugenio Bianchi, Carlo Rovelli & Rocky Kolb, modifications by me.
Image credit: Eugenio Bianchi, Carlo Rovelli & Rocky Kolb, modifications by me.

But on the other hand, the Universe is not only expanding, but that expansion is accelerating, thanks to the presence of dark energy, an intrinsic energy to empty space itself.

Image credit: Large Synoptic Survey Telescope, NSF, DOE, and AURA.
Image credit: Large Synoptic Survey Telescope, NSF, DOE, and AURA.

But if space is expanding, then aren’t we simply making new, empty space out of nothing, when there was none before? And wouldn’t that violate the conservation of energy?

Go and find out here!

29 thoughts on “Is energy conserved in a Universe with dark energy? (Synopsis)

  1. the evidence we have for an expanding universe – red shift

    what if the reason for red shift was that the speed of light was faster in inter galactic space – by which i mean the speed of light is always relative to the total gravitational forces at the point it is measured

    we can only measure the speed of light where we are – two space craft travelling in different directions sending messages to each other across space might send us back info on what they think the speed of light is

    so many unexplained phenomena might be resolved if we let C vary according to the sum of gravitational forces at the point it is travelling through

    as light enters our galaxy it is slowed down by the gravity of our galaxy – and we get red shift

    as it leaves our galaxy it speeds up – effectively blue-shifting until it reaches some gravitationally denser region

    can you explain why this silly idea is not viable?


  2. @Ethan: Skimmed Carroll et al.’s excellent Ann.Rev. paper (it’s great that it isn’t behind a paywall!). One thing I noticed is that you only get the energy balance you’re touting for the special case of P = -rho (equivalently w = -1), corresponding to Einstein’s “classic” cosmological constant.

    It looks to me (and I am *NOT* a theorist!) like the more dynamical models inspired by field theory don’t get you the same energy balance. Is this something you know enough about to address, either in detail or by referring me to something a poor experimentalist can understand?

  3. I’m not sure that I understand everything but in the end, could we say that your explanation brings in symmetry?

  4. This is a good question, but I think there are already potential issues “in principle” with energy conservation in the universe as a whole. Here’s a paradox I thought of years ago, similar to some other things written about mostly later; see review at imagine the universe (just as a “given,” forget how) filled with a network of “devices” and connecting elastic bands or cables that are momentarily (at the cosmic time we now consider) just extended but not stretched. The devices are arrayed in a 3-D Cartesian grid, and all connected to their nearest neighbors (hence, they are like the corners of a jungle gym and the cables are like the rods.) If the universe is expanding, these cables will stretch and build up elastic energy *in proportion to their elastic constants k* (yes I know there must be a limit), which is independent of mass, G etc.

    Consider that as the universe expands, the devices separate further and the cables get stretched and pick up elastic energy U = ks^2/2. Where does this energy come from? In an ordinary case, something is independently *pulling* on each end of the cable and applying work from outside. However, in the universe things are symmetrical. Every device is pulled on six sides by its neighbors! Each one is subject to zero net forces and continues to separate according to Hubble rules. The strings don’t “need” someone to pull from the outside and do the work. So there is a paradox here about energy conservation. (Yes, a paradox of understanding, even if somehow the energy would come out of something else in truth – but from what?) I wrote about this at my blog: cosmic energy paradox.

    Also, what happens when the strings reach maximum extension? There are other paradoxes of symmetry about attempts to physically enclose, block, or rigidify the points that are supposed to be uniformly receeding or contracting. I won’t go into detail here, but consider if hard bubbles try to compress in an infinite symmetrical universe: if they are stopped, there are contradictions about what should happen to enclosed test bodies, contradictions about centering of gravitating shells, etc.

  5. Well, I have the feeling that we don’t really know what “space(-time)” really is, and that makes it somewhat premature to be so relatively (no pun intended) certain about how it behaves and will behave in the future.

    The real nature of space-time compared to the way we normally think about it, is as general relativity is to newtonian physics. I think. Or like the way we can usually calculate the behaviour of gasses without accounting for the individual atoms, because we’re usually operating on larger scales, where the behaviour of atoms average out into simpler formulas.

    The idea of a smooth more-or-less 4-dimensional space-time is just a working assumption on the scales we normally deal with. Whenever I hear the word “field”, I’m beginning to think, this is just an approximation, not the real nature of space-time. space-time is (I suspect) discrete somehow, and “fields” are an approximation that doesn’t work on the smaller scales.

    I remember reading about the idea of space-time possibly undergoing phase transitions (in the past, or in the future), and also the idea that the 4 dimensions we see today are not fundamental, but an emergent phenomenon (if space-time is curved, does this mean that, if one allows for fractional dimensions, the dimensions are really 4 -/+ epsilon, where epsilon is sort-of related to the curvature ?)

    Google found this, for instance:

    I’d like feedback on this. I’m not a crackpot with some idée fixe, just someone who likes to think about things even though I lack formal education in the field.

  6. @Neil Bates

    ” If the universe is expanding, these cables will stretch and build up elastic energy”

    no, they won’t. It’s spacetime that’s expanding, not the matter content in it. Matter will “flow”, caught in spacetime, if there are no other forces acting on it. Since your wires or rods or whatever are held together by atomic forces, that “network” grid you are talking about will just sit there. It might colapse on itself due to gravity. But expansion won’t do anything to it.

  7. Ethan: no problem with conservation of energy, but I think one can go further.

    Physicists talk about the bag model. Quarks are said to be hard to separate, like they’re inside an elastic bag. Where does this gluonic “elastic tension” go in low-energy proton-antiproton annihilation to gamma photons? And what keeps a photon, a singleton electromagnetic wave, propagating at c? Answer, it doesn’t go anywhere, it’s an aspect of space. And if space didn’t have this quality, waves wouldn’t run through it.

    Cosmologists talk about the balloon analogy. A balloon is the size it is because the internal pressure is counterbalanced by the tension in the skin. Now, how do you make that balloon bigger? You can blow some more air into it. That’s like adding more energy, increasing the pressure. But as we know, when it comes to the universe, that’s creation ex nihilo. That drives a coach and horses through conservation of energy. But there is another way to make that balloon bigger: reduce the tensile strength of the skin. Think bubblegum. Tension is negative pressure and when you reduce the tension the balloon gets bigger until the internal pressure is reduced and balances the tension again. But the balloon got bigger so the skin is now thinner so the tensile strength is reduced again, so the balloon gets bigger again.

    And so it goes, the universe expands, and that expansion doesn’t stop, because as space expands the “strength of space” reduces. See page 5 of where Milgrom mentions elasticity and strength when he refers to f(R) gravity. Also see papers by John Webb et al. How does it all end? You might want to have a look at this by Phil Plait.

  8. well i think there are a lot of ways to look at things and each explored in turn will reveal something new but…
    you need the math to go with it and some theory’s most or variations of existing ones with important twists need a proper explanation and visualization i.e. put into words clearly
    and all the important points and variable points need to be defined as such so that they can be explored and they have to be conveyable to others in words clearly or they are literally meaningless
    (so as the saying goes in a different light choose your words carefully to express your thoughts clearly)

  9. Neil Bates, your paradox about the elastic is a good one. If they stretch far enough (say over the entire observable universe) then they will indeed continue to stretch and build up energy as the universe expands. In fact this is similar to the effect of the cosmological constant and the resolution is the same. The elastic would do negative work on spacetime causing it to accelerate faster (not slower as you might intuitively think) If the elastic has a stretch limit it will simply break when that limit is reached. Materials of unlimited strength are forbidden by relativity.

    Michael Kelsey, if dark energy is a dynamic field rather than a cosmological constant then that field would have to have its own dynamics that would account for energy balance. Provided the dynamics are derived from a principle of least action with no explicit time dependence (as all known laws of physics are) then there will automatically be an energy conservation law by Noether’s theorem.

    See also on conservation of energy in GR covering many points including the cosmological constant paradox discussed here (point (2) in the paper).

  10. Philip: that is worth looking into but I don’t see how the elastic energy (which builds up as the square of the extra distance moved since the reference time when the cables are extended at just normal length, and is also dependent on elastic constant) is quantitatively and in general counterbalanced by something else. Also I still don’t get why increased energy in the cables would be balanced by even greater acceleration of the bodies in that cosmos. Dark energy is like a negative mass that produces positive gravitational “field energy” (altho that is misleading) much as positive mass is supposed to produce negative GFE equivalent.

    Note too the squared progression (within a range that indeed can’t be maintained, I am focusing on the Hooke domain.)

    Compare Sean Carroll who here just says flat out, that it’s better to say energy is not conserved (altho it’s game to try and get that resolved, no necessity to accept that status quo and your points should be looked at):

  11. Ethan, thanks for the comment section here, this is a good solution. Hey, I can’t get past this bit: “You’ve got this sphere-like object expanding, and there you are, this constant energy density (i.e., dark energy), and you fill the sphere. You’re positive energy. You’re gravitationally pulling this sphere in on itself.” Why is the way you put it the opposite from the usual account, where gravity pulls inwards but the energy of empty space pushes outwards and ultimately “wins”? I can’t understand why you say dark energy gravitationally pulls the sphere in on itself. Why not say instead that it’s gravity that is pulling inwards and is therefore doing negative work as the universe expands despite gravity, and that negative work is what allows “new” energy to be created?

  12. @John Duffield #9: Addressing only your first point, you ask where the energy (“tension”) in the gluon field goes when protons annihilate. The answer is nearly trivial — that energy goes into the outgoing photons!

    Frank Wilczek has done a great job (especially in Physics Today “Reference Frame” columns) of pointing out the narrowness of the “Higgs is where mass originates” canard :-). For all of the matter we encounter every day, nearly all of the mass (of the protons and neutrons) comes from the gluons binding up the quarks in the nucleons.

    We know (basically from the pattern of masses of pi, rho, sigma and related mesons) that the “light quarks” (up and down) have masses of just a few MeV. How does three times a few MeV turn into the GeV mass of protons and neutrons? As Wilczek points out, its the energy of the gluon field which makes up the difference. A bit of “Zeeman splitting” analogue from the broken isospin symmetry, gets you the proton/neutron difference (otherwise, they’d have the same mass).

  13. @Philip Gibbs #11: Hmmm. Yeah, I suspect you’re right. As something like, let’s say, a “slow-roll inflaton”, has its mass run down from the original high-energy state down to the broken-symmetry ground state, that energy has to go somewhere. It must go into the expansion which the slow-roll is driving.

    I guess I’d feel happier seeing the energy balance explicitly derived, the way Carroll et al. did for the P = -rho case; but that’s just me being an experimentalist :-/

  14. im going to point this out simply here as i think there are people that will understand what im saying viewing

    when we look at that example model of the balloon what we are really saying is this … empty space is expanding and its taking mass with it yet mass is not flat to it topologically ….
    now that said it can be viewed as happening in one of the following ways and that is the only question being explored
    the first is not under discussion currently in science except at the furthest fringes
    so what is the discussion how is space performing expansion ?
    here are some implicit presuppositions…

    that matter is not composed of the same stuff outside it
    such that it doesn’t shrink to say matter is not space time
    or viably that it is but doesn’t somehow follow the same rules as this supposed dark energy / empty flat space
    but that it instead rides on it like a boat in stream that is ever increasing in speed and that space time is expanding or fabric field whatever you like,
    seems a little far fetch and with that view throw away unification

    or we can view it such
    that it mass is composed of flat space time but it is twisted up dimensionally all its parts/components locations is not in the same local flat space-time as the relatively flat space-time outside of it
    that geometrical totality causes the local space nearby to distort in compensation of the warping
    yet of importance is the previous comparison that the expansion of matter to the flat space time in not at equal angles in the traditional sense of space and in that sense it expands slower in our dimensional view yet proportionally
    and equivalently when more dimensions are accounted for

    so from that view mass is actually expanding at the same rate as it is composed of the same thing but due to the angular difference dimensionally not expanding at the same rate as the in the plane of the relatively flat empty space-time so you get the exact same effect
    both of these present real problems
    both views have Equal Problems
    at the edges of the universe as this acceleration of space and time itself then must at some point exceed the speed of light and fall off the proverbial universe cliff
    that would be a problem

    conversely….we might look at two less thought of possibilitys
    if we say that space-time fully apply’s to matter but the dimensional effects of time are multiple and complex then we might say that in a certain model
    we need not expand the universe but view it as a contracting one separate from gravity or with gravity as simply a acceleration of this contraction on a flat space-time
    …were matter itself is contracting faster ..then empty space time because…
    there is more space time in matter then in empty space which will give the exact same perspective as the expanding universe in the second example
    to the observer they will be equivalent

    so you still need special math to look at mass as a distortion on the relatively flat space time

    in some ways this is actually easier to view it this way
    as the whole of the universe contracting
    as gravity might be viewed as a acceleration of this ever present effect
    as this is actually parallel to using zenos paradox for calculations were the universe is literally acting like a oracle turing machine

    there is also then the very first question of is the universe even really expanding as if we look at multi dimensional time we see that we maybe fooled by curved emission observation energy’s not being fully imparted into electrical signal energy due to a literal 3d time arrow component discrepancy possibly inherit in matter some are working on this now to explore it mathematically and so far its looking like it solves many problems

  15. now there is no edit button so let me add
    take a real balloon with two knots in it as you blow it up the knot doesn’t expand but it is the same material ask yourself why also ask is the surface of the balloon in truth expanding
    if you could view its surface side on microscopically you would see it is in fact contracting getting thinner in one dimension
    to make up for the expansion along the other consider now
    a balloon that thickens as it expands in that manner and reverse the idea as you let the air out exact same thing
    exact same knot cause and effect dimensionally the knot is not entirely on the surface

  16. @ Neil & Gibbs

    again.. I urge you to read up on your relativity and expansion, since what you write about stretching of physical objects is physically incorrect.

    concerning Noether theorem and DE. DE is constant in space. It is not constant in time. There will be a conservation law tied to that field once we know what it is and how it works. What it needn’t be is conservation of energy. It could be conservation of charge just as well… since we don’t know the exact dynamics and properties of DE field.

  17. p.s.

    “Dark energy is like a negative mass ”
    No, it’s like negative pressure. Very different things.

    “a “slow-roll inflaton”, has its mass run down from the original high-energy state down to the broken-symmetry ground state, that energy has to go somewhere. It must go into the expansion which the slow-roll is driving. ”
    -That energy goes to particles and reheating. Not expansion. The universe is exponentially expanding while the potential is at it’s highest, as it begins to drop, that difference is transferred to matter, not expansion again.

  18. Michael #14: you misunderstood what I was saying. If you can find a rubber mat, give it a shake. A wave runs through it because it has an elastic nature. A photon is a wave, E=hc/λ applies, space has an “elastic” nature too. The gluon field doesn’t magically switch off in low-energy proton-antiproton annihilation to gamma photons. It’s still there, in space, where the photon is, and everywhere else. There’s a deep connection between the bag model and the balloon analogy. And there’s two ways to make that balloon bigger.

  19. dark energy is a term coined to universal expansion via the problem that red shift increases as star distance increases
    as if the entire fabric of space were being streached across the universe yet matter is not inflating at the same rate

    dark matter is a term coined because the observation of the speed of the stars at the edge of the galaxy doesn’t make sense as to why they have simply not been flung off
    they appear to be moving at the same speed across the disc which is impossible so some smart dumb guy went oh there must be invisible mass a whoooole lot of it that no one can see its invisible its dark mass

  20. @Will

    “dark energy is a term coined to universal expansion via the problem that red shift increases as star distance increases”

    – no. That’s Hubble constant. DE was coined to explain the acceleration of that expansion in the last couple of billion years. And also the flatness problem.

  21. Apart from being a good article, I still have some remarks on the text:

    ¨It’s expanding, and it’s expanding outwards. In other words, you’re (gravitationally) pulling inwards, which is the opposite direction as the expansion, and so you’re doing negative work!¨.

    If the gentleman in the first picture (aka Mr. Dark Energy) is lifting the book up against gravity there is an 180o angle between the force and displacement. The work done by mr. D. Energy is positive but the work done by the gravitational force on the book is negative.

    – Which force is described here exactly (in the word ¨you’re¨)?
    I think it is obviously referring here to mr. D. Energy. So far so good.

    But later on in the text:

    ¨….In other words, you’re (gravitationally) pulling inwards, which is the opposite direction as the expansion, and so you’re doing negative work!¨

    In this case the words ¨you’re¨ seems to refer to the gravitational force. Which is not referring to mr. D. Energy anymore. The work done by the gravitational force on the stars would be negative, but the work done by dark energy should be positive.

    So I don understand there what you mean exactly. I suppose that the confusion here comes from the fact that there are 2 different viewpoints being used. The starting point should always be the force applied to the object.

    When you look at the universe from the INSIDE dark energy is a positive force. But when looked at it from the OUTSIDE (like a god) it is possible to talk about the pressure on the sphere. Vacuum energy has negative pressure, which acts as “negative work” to absorb this apparent creation of energy.

  22. Sorry, while copying something went wrong.
    The first text in quotes should be:

    ¨YOU’RE positive energy. YOU’RE gravitationally pulling this sphere in on itself.¨.

    I forgot to mention also that I am referring to the text on

  23. If light is red-shifted due to the expansion of space, then must we assume that the expansion must physically occur in the region of space in which the light is currently travelling, stretching out the light in the process?

    If space is discrete instead of continuous, would this give rise to any measurable effects in the red-shifting?

  24. Wait a second (that’s a long time)… People talk about an expanding universe and that is fine but I think there is a lot of faith being put in the current theories and then constants and hypotheses are created in an attempt to explain what perhaps does not exist or is not the case… like trying to fit a size 10 foot into a size 4 shoe…. and making lots of tests and maths to do so.

    I ask a question: if the universe is expanding, what is it expanding into? E.g. what is outside of the universe? Empty space can’t expand into empty space right?
    All the Einstein equations and the work of scientist on Earth might merely just be explaining side effects of a bigger picture, one affected by what is supposedly outside of the universe.

    Here is another view: I get the feeling people see the big bang as the beginning of the universe… like a spark that started it all. What was there before? but also, in regards to expansion itself, what if the big bang was actually so big, like a huge explosion that threw stuff in all directions at incredible, unimaginable force (just like any bomb but much grander), and the expansion we are seeing is just part of that… we are still in the expanding because the explosion aftermath is still going. In other words, no dark energy, just the aftermath of the explosion which naturally expands all physical matter within it.

    Yet another question: What is holding celestial bodies/planets up? and don’t say “spacetime”.

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