Is the Higgs Field Vacuum Energy Density Negative?

[deneve]

The following is from a research paper:

doi:10.1088/0034-4885/68/4/R04
The structure of the world from pure numbers
F J Tipler
Department of Mathematics and Department of Physics, Tulane University, New Orleans,
LA 70118, USA
Received 21 September 2004
Published 15 March 2005
Online at stacks.iop.org/RoPP/68/897

I quote from page 959 of the paper





"What I shall now do is describe the physical mechanism that will eventually neutralize the observed currently
positive effective cosmological constant. (See Peebles and Ratta 2003 for a recent review
of the observations suggesting that the Dark Energy is in fact an uncancelled cosmological
constant.)
It is well known that the mutual consistency of the particle physics SM 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 ∼−1.0 × 1026 gm cm−3 (mH/246) GeV, where mH is the Higgs boson mass,
which is 114.4 GeV < mH < 251 GeV at the 95% confidence level (Abazov et al 2004).
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 to power−29 omega total x h to power 2 gm cm−3, and observations (Spergel et al 2003)
indicate that omega total = 1.02 ± 0.02 and h = 0.71 ± 0.04, 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 am intrigued by this and wonder if anyone can help me understand it. First and foremost He seems to be saying that the vacuum energy density is NEGATIVE. Classically I presume he is saying that the mexican hat potential for the higgs field potential has its maximum at zero and its minima at some less than zero value. How do we know this has a negative value? Would this not mean that the Dominant Energy condition of Hawking and Ellis is violated by the Higgs field since this condition requires energy density to be greater than or equal to zero? However, he certainly thiks it is negative , otherwise you would not get a positive pressure for it from the equation of state. I am puzzled but intrigued at the possibility of a quintessence like decaying Cosmological constant but I don't know how to see that the vacuum energy for the higgs field is negative. My particle physics knowledge is very poor so any help with this one would be gratefully accepted

 

[Drakkith]

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[Drakkith]

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