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Dark energy <=> negative energy?

  1. Dec 1, 2011 #1
    Sorry if this sounds a bit mixed up.

    When I was growing up, in the late 1990's, popular science books about cosmology use to describe the average mass-energy density of the universe, especially comparing it to the critical density. Those books used to say that visible matter gives too-low density, but astrophysical evidence show that there is some other stuff out there that brings the density close to the critical value. IIRC, that's what called now "dark matter".

    Does this relate to dark energy at all? I see two conflicting points here:
    1. Dark energy is said to be similar to the cosmological constant. The effect of that is similar to spreading a uniform negative mass over the universe.
    2. Dark energy is said to account for 73% of the total mass-energy of the universe.

    I'm only a mathematician, and never learned GR formally, but these seem to conflict - is the energy of dark energy positive of negative?

    As an additional question, I would like to ask how the 73% estimate was computed.
    My guess is that the intensity of CMB radiation was measures, and the mass-energy density inferred from its temperature only gave 0.27Ω. Is this the way it's done?
  2. jcsd
  3. Dec 1, 2011 #2


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    For terminology about distance measures google "hogg distance" or go to

    For a tutorial on Lambda with some discussion of how it was measured see

    there is a picture with two tear-drop diagrams. In one the expansion worldlines show slowing expansion, in the other with positive Lambda they do not show slowing and are even bending outwards after a while, (very slight accelerated spreading).

    He asks you to consider supernovae at z=1. They are DIMMER than expected by 84% which means they are FARTHER than expected (with zero Lambda) by 36%.

    That kind of data is part of what told cosmologists that Ωλ = .75 approximately, or as you say .73. they keep refining it.

    For more see the intersecting ovals diagram that comes before the tear-drop figure.

    He explains how the different kinds of data constrained the pair (Ωλ , ΩM down to the yellow strip (by Supernovae data) and then from there down to the small purple region (using other data.)
    Last edited: Dec 1, 2011
  4. Dec 2, 2011 #3
    Thanks a lot for the info, it really answered my questions.
    The cosmology tutorial is especially helpful. (it's also interesting to learn that the CMB measurements tell us the universe is closed)
  5. Dec 2, 2011 #4

    Ken G

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    In case those tutorials didn't answer this for you, there is a fairly simple answer to this. The cosmological constant is not like a uniform negative mass or negative energy-- it is positive energy all the way (hence point #2). The trick is, in general relativity gravity does not just come from rest mass (and hence rest energy), it also comes from pressure. Usually the pressure contribution is negligible-- like the way the pressure of the Sun contributes to its gravity is totally swamped by the way its rest mass contributes to its gravity. But that's because the Sun is mostly nonrelativistic gas-- dark energy is working in a highly relativistic way, whatever is causing it. Now, in unusual situations (like with vacuum energy), pressure can not only be important to gravity, it can be related to energy in weird ways-- in particular, it can be negative when the energy is positive!

    The reason for this is that pressure is basically how much energy you can remove from a system when you expand it a given tiny amount, but to expand vacuum, it requires more vacuum-- which if vacuum holds energy, requires that you add energy! So you don't extract energy when vacuum expands, you need to add it instead. That means the pressure of vacuum is negative if there is vacuum energy, and that means its gravity is negative too-- so not negative mass or negative energy, but negative gravity (or "antigravity"). So two masses placed far enough apart actually experience of a kind of repulsion-- due to the vacuum between them. (And all of this is contingent on there being a cosmological constant, which is a simple explanation for the accelerated expansion but by no means the only explanation.)
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