A vanishing cosmological constant in elementary particle theory

The quest of a vanishing cosmological constant is considered in the simplest anomaly-free chiral gauge extension of the electroweak standard model where the new physics is limited to a well defined additional flavordynamics above the Fermi scale, namely up to a few TeVs by matching the gauge coupling constants at the electroweak scale, and with an extended scalarland. In contrast to the electroweak standard model, it is shown how the extended scalar sector of the theory allows a vanishing or a very small cosmological constant. The details of the cancellation mechanism are presented. At accessible energies the theory is indistinguishable from the standard model of elementary particles and it is in agreement with all existing data. PACS numbers: 12.15.Cc: Extensions of gauge or Higgs sector; 98.80.-k: Cosmology Typeset using REVTEX ∗Address after March 1997: Instituto de F́ısica, Universidade Federal do Paraná, 81531-990, Curitiba, PR, Brazil 1 All astronomical surveys agree that there is no evidence for any spacetime distortion due to a nonvanishing cosmological constant [1] which is many orders of magnitude smaller than that estimated in theories of elementary particles. Up to distances which are accessible to astronomers, about 10 billion light-years, or 10 cm, the magnitude of the cosmological constant must be smaller than 10 cm ≈ 10GeV. The possible presence of the cosmological constant Λ in the Einstein’s field equations Rμν − ( 1 2 R− Λ ) gμν = 8πG c Tμν (1) can eventually be vindicated by measuring exponential deviations from the standard matter dominated spatially flat Friedman-Robertson-Walker universe scale factor R(t) ∼ t. The influence of matter on the metric is determined by the energy-momentum tensor Tμν . The component T00 is the energy density and the coefficient c /8πG ≈ 5× 10 g× cm× sec, where G is the Newtonian gravitational constant, measures the elasticity of the vacuum. The cosmological constant is, according to astronomical evidence, very close to zero. There is no understanding of why Λ should be close or equal to zero. This question of the cosmological constant problem, which consists in understanding a possible cancellation, is widely regarded as one of the most significative mysteries of the modern cosmology. A proposal for solution, due to Baum-Hawking-Coleman [2], has attracted much attention. It argues that the vanishing of the cosmological constant is closely related to a wormhole-induced quantum instability of the theory. The observable value of the cosmological constant could not be an absolutely fundamental c-number parameter but a dynamical quantum variable with the meaning of topological changes, such as baby universes and wormholes [3]. Nowhere, in physics, we find a greater divergence between theory and experiment than in the cosmological constant problem. As emphasized by Weinberg [4], for a particle physicist, all the values in the observationally allowed range, extending up to values that would make up most of the critical density required in a spatially flat Robertson-Walker universe, seem ridiculously implausible. We should remark that all the standard cosmological model is faced by a severe hierarchical problem, the vacuum energy of the actual universe is extremely fine tuned to 2 zero [5]. In elementary particle theory the underlying gauge symmetry is larger than that of the actual vacuum whose symmetry is the combination of the color and the abelian electromagnetic factors G3C1em ≡ SU(3)C ⊗ U(1)em. The full gauge symmetry of the standard model for the nongravitational interactions [6] G3C2L1Y ≡ SU(3)C ⊗ SU(2)L ⊗U(1)Y is restored at the Fermi scale ΛF = 1 21/4 √ GF ≈ 246GeV (GF ≈ 1.166 × 10−5GeV) equivalent to a time of order 10 sec. This scale is set by the decay constant of the three Goldstone bosons transformed via the Higgs-Kibble mechanism [7] into the longitudinal components of the weak gauge bosons. The underlying G3C2L1Y symmetry is not manifest in the structure of the vacuum and nature realizes the mechanism of spontaneous symmetry breaking G3C2L1Y → G3C1em where the G3C2L1Y symmetry is broken because the associated vacuum state is not invariant anymore. Spontaneous symmetry breaking preserves the renormalizability of the original gauge theory even after symmetry breaking, giving us a renormalizable theory of massive vector bosons [8]. Let us consider a scalar field with a φ interaction L = ∂μφ∂φ− V (φ); (2) V (φ) = − 2 mφ + 1 4 λφ containing the discrete symmetry φ → −φ, L(φ) → L(−φ) = L(φ). In the electroweak standard model with the multiplet of scalar fields transforming under G3C2L1Y as Φ ≡ 