On the smallness of the cosmological constant

Abstract

In N = 1 supergravity the scalar potential of the hidden sector may have degenerate supersymmetric (SUSY) and non-supersymmetric Minkowski vacua. In this case local SUSY in the second supersymmetric Minkowski phase can be broken dynamically. Assuming that such a second phase and the phase associated with the physical vacuum are exactly degenerate, we estimate the value of the cosmological constant. We argue that the observed value of the dark energy density can be reproduced if in the second vacuum local SUSY breaking is induced by gaugino condensation at a scale which is just slightly lower than Λ QCD in the physical vacuum. The presence of a third degenerate vacuum, in which local SUSY and electroweak (EW) symmetry are broken near the Planck scale, may lead to small values of the quartic Higgs self-coupling and the corresponding beta function at the Planck scale in the phase in which we live.

Cosmological Constant in SUGRA Models with Degenerate Vacua

“…Because of the postulated exact degeneracy of vacua, the physical phase, in which SUSY is broken near the Planck scale, has the same energy density as the phase where the breakdown of local SUSY is induced by the gaugino condensate in the hidden sector. Then, from Equation (37), it follows that the measured cosmological constant can be reproduced if Λ X is somewhat close to Λ QCD in the physical vacuum [21][22][23][24], i.e., Λ X ∼ Λ QCD /10 .…”

“…Although there is no compelling reason to expect that the two scales Λ X and Λ QCD should be relatively close, Λ QCD and M P can be considered as the two most natural choices for the scale of dimensional transmutation in the hidden sector in the second phase. In the case when the non-Abelian interactions, which lead to the formation of the gaugino condensate in the hidden sector, are described by SU(3) SUSY gluodynamics, the corresponding value of Λ X can be obtained if the SU(3) gauge coupling g X (M P ) ≈ 0.65 [21][22][23][24]. This is just slightly larger than the value of the QCD gauge coupling at the Planck scale in the SM, i.e., g 3 (M P ) ≈ 0.49 [1].…”

“…The successful predictions for the Higgs and top quarks masses (5) suggest that the MPP can be used to explain the tiny dark energy density spread all over the Universe (the cosmological constant ρ Λ ), which is responsible for its accelerated expansion. In previous articles [12][13][14][15][16][17][18][19][20][21][22][23][24], the implementation of the MPP in models based on local supersymmetry, supergravity (SUGRA), was studied. In SUGRA models a huge degree of fine-tuning is required to ensure that the energy density in the physical vacuum is sufficiently small.…”

“…In SUGRA models a huge degree of fine-tuning is required to ensure that the energy density in the physical vacuum is sufficiently small. The successful application of the MPP to (N = 1) supergravity implies the existence of a vacuum in which the low-energy limit of the theory is described by a pure supersymmetric model in flat Minkowski space [12][13][14][15][16][17][18][19][20][21][22][23][24]. According to the MPP, the physical vacuum is the one in which we live, and this second vacuum must have the same vacuum energy density.…”

“…However, in the second vacuum, the dynamical breakdown of SUSY may take place, leading to an exponentially-suppressed value of the vacuum energy density. This energy density is then transferred to the physical vacuum by the assumed degeneracy [12][13][14][15][16][17][18][19][20][21][22][23][24]. The results of the numerical analysis performed in the previous works indicate that in the leading one-loop approximation, the observed value of the cosmological constant can be reproduced, even if the SM gauge couplings are almost identical in both vacua.…”