Abstract
and H0 = (ȧ/a)0 is the Hubble constant in the present era, with a(t) being the Friedmann-Robertson-Walker scale parameter [4, 6]. Long before the current period of precision cosmology, it was known that ΩΛ could not be larger than O(1). In the context of quantum field theory, this was very difficult to understand, because estimates of the contributions to ρΛ from (i) vacuum condensates of quark and gluon fields in quantum chromodynamics (QCD) and the vacuum expectation value of the Higgs field hypothesized in the Standard Model (SM) to be responsible for electroweak symmetry breaking, and from (ii) zero-point energies of quantum fields appear to be too large by many orders of magnitude. Observations of supernovae showed the accelerated expansion of the universe and are consistent with the hypothesis that this is due to a cosmological constant, ΩΛ ≃ 0.76 [7, 8, 9]. Here we shall propose a solution to the problem of QCD condensate contributions to ρΛ. We also comment on other contributions of type (i) and (ii). Two important condensates in QCD are the quark condensates 〈qq〉 ≡ 〈∑Nc a=1 qaq〉, where q is a quark whose current-quark mass is small compared with the confinement scale ΛQCD ≃ 250 MeV, and the gluon condensate, 〈GμνG〉 ≡ 〈 ∑N2 c −1 a=1 G a μνG aμν〉, where Gμν = ∂μAν − ∂νA a μ + gscabcA b μA c ν , a, b, c denote the color indices, gs is the color SU(3)c gauge coupling, Nc = 3, and cabc are the structure constants for SU(3)c. These condensates form at times of order 10 sec. in the early universe as the temperature T decreases below the confinementdeconfinent temperature Tdec ≃ 200 MeV. For T << Tdec, in the conventional quantum field theory view, these condensates are considered to be constants throughout space. If this were true, then they would contribute (δρΛ)QCD ∼ Λ4QCD, so that (δΩΛ)QCD ≃ 10. However, we have argued in Ref. [13] that, contrary to this conventional view, these condensates (and also higherorder ones such as 〈(qq)2〉 and 〈(qq)GμνG〉) have spatial support within hadrons, not extending throughout all of space. The reason for this is that the condensates arise because of quark and gluon interactions, and these particles are confined within hadrons [14]. We have argued that, consequently, these QCD condensates should really be considered as comprising part of the masses of hadrons. Hence, we conclude that their effect on gravity is already included in the baryon term Ωb in Ωm and, as such, they do not contribute to ΩΛ. Another excessive type-(i) contribution to ρΛ is conventionally viewed as arising from the vacuum expectation value of the Standard-Model Higgs field, vEW = 2G −1/2 F = 246 GeV, giving (δρΛ)EW ∼ v EW and hence (δΩΛ)EW ∼ 10. Similar numbers are obtained from Higgs vacuum expectation values in supersymmetric extensions of the Standard Model (recalling that the supersymmetry breaking scale is expected to be the TeV scale). However, it is possible that electroweak symmetry breaking is dynamical; for example, it may result from the formation of a bilinear condensate of fermions F (called technifermions) subject to an asymptotically free, vectorial, confining gauge interaction, commonly called technicolor (TC), that gets strong on the TeV scale [15]. In such theories there is no fundamental Higgs field. Technicolor theories are challenged by, but may be able to survive, constraints from precision electroweak data. By our arguments in [13], in a technicolor theory, the technifermion and technigluon condensates would have spatial support in the technihadrons and techniglueballs and would contribute to the masses of these states. We stress that, just as was true for the QCD condensates, these technifermion and technigluon condensates would not contribute to ρΛ. Hence, if a technicolor-type mechanism should turn out to be responsible for electroweak SLAC-PUB-13166
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