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The link between the cosmological constant and the higgs field

  1. May 12, 2007 #1
    I have read that the current expansion of the universe could be due to a bare positive cosmological constant along with a negative cosmological constant due to the false vacuum of the higgs field. Currently this negative CC is not enough to cancel the positive cc but with time this can be changed via electroweak tunnelling. Now whether this is the actual case or not is one issue but I want to understand the argument. Firstly the usual value of the cc due ro a dynamic scalar field (quintessence or inflaton) is due to a negative pressure which is equal to the negative of the energy density of the potential that is slowly rolled over. Note that the energy density is NOT negative here although the pressure is. Now if what I've read is correct then the implication is that there are potential curves for the higgs field which entail the energy density going negative. I guess this means the true vacuum is below zero energy and the rim of the "mexican hat" is negative or below zero. I don't really know anything about particle physics so I need some help here - Usually the datum for potential energy is a matter of convenience so I am not sure how to understand negative vacuum energies - how are they manifest and what fixes the zero level of energy density anyway. Can anyone help me to look at this the right way. I have a research degree in cosmology but my background in particle physics is bad so any help would be gratefully recieved.
  2. jcsd
  3. May 13, 2007 #2


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    Looking at the high energy realm is difficult, even in particle physics. And our equipment is trifling compared to the high energy universe. Culling that data is difficult.
  4. May 13, 2007 #3


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    Hi deneve and welcome to these Forums!

    All we do know is the universe appears to require a component of non-interacting, or weakly interacting, non-baryonic Dark Matter and a component of negative pressure Dark Energy, the DE may or may not be the signature of a cosmological constant or vacuum energy or something else.

    In fact most of the universe's mass appears to be in these two mysterious forms: 4% baryonic matter, 23% non-baryonic Dark Matter and 73% Dark Energy.

    While these dark components are yet to be discovered 'in the laboratory' theories abound about what they are and any viable proposal is as good as any other.

    Last edited: May 13, 2007
  5. May 13, 2007 #4


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    My guess is that you cannot rule out a shape for the Higgs potential that goes down to a negative energy minimum. When doing QFT energy scales are not really relevant because one is free to define the vacuum and set up a definition of observed particles. However, gravity differentiates between positive and negative energies and makes it impossible to rescale energies due to the different behaviour of space-time depending on the energy content. Assuming that the Higgs might be in a negative energy minimum, then the cosmological scenario is as you have described. I cannot help you with the current constraints or value for the Higgs, but I share with you my interest in knowing how far a negative value for the ground state energy could arise naturally in the calculations. I mean, you have a negative vev for the Higgs field (assuming m2 < 0) but the question is if the Hamiltonian H = T00 for the ground state is a negative value as well.
    Last edited: May 14, 2007
  6. May 15, 2007 #5


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    The ground state cannot go below zero without new physics.
  7. Jun 22, 2007 #6
    I'm still stuck with negative vev's

    Tipler arXiv:astro-ph/0111520v1 quotes on page 29 that "...It is well-known that the mutual consistency of the particle physics Standard Model and general
    relativity requires the existence of a very large positive cosmological constant. The reason is simple:
    the non-zero vacuum expectation value for the Higgs field yields a vacuum energy density of about −1.0 × 10^26 gm/cm3(mH/246)GeV, where mH is the Higgs boson mass. Since this is a negative vacuum energy, it
    is accompanied by a positive pressure of equal magnitude, and both the pressure and energy yield a negative
    cosmological constant. Since the closure density is 1.88×10−29
    0h2gm/cm3, and observations indicate that

    OMEGA0 = 1 and h = 0.66, there must be a fundamental positive cosmological constant to cancel out the negative
    cosmological constant coming from the Higgs field. What we observe accelerating the universe today is the
    sum of the fundamental positive cosmological constant, and the negative Higgs field cosmological constant;
    this sum is the “effective” cosmological constant."

    I just don't quite know what to make of this it all makes sense except that he thinks the vev is negative???

    Can any one suggest an explanation.
  8. Jun 23, 2007 #7
    I am not sure if I understand correctly, but I think he is saying that the higgs mexican hat potential has to be compensated by a negative cosmological constant which when calculated yields -10^26 g/cm3. Because the observed value is 10^-29 g/cm3, he says that this correponds to adding a positive cosmological constant of 10^26 g/cm3 - 10^-29 g/cm3

    ...quite unatural.... why don't they simply cancel out, why do they leave just 10^-29. Makes you wonder if the Higgs field really exists...
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