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We suggest a solution to the problem of some apparently excessive contributions to the cosmological constant from Standard-Model condensates.
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String theory has no parameter except the string scale $M_S$, so the Planck scale $M_text{Pl}$, the supersymmetry-breaking scale, the EW scale $m_text{EW}$ as well as the vacuum energy density (cosmological constant) $Lambda$ are to be determined dynamically at any local minimum solution in the string theory landscape. Here we consider a model that links the supersymmetric electroweak phenomenology (bottom up) to the string theory motivated flux compactification approach (top down). In this model, supersymmetry is broken by a combination of the racetrack Kahler uplift mechanism, which naturally allows an exponentially small positive $Lambda$ in a local minimum, and the anti-D3-brane in the KKLT scenario. In the absence of the Higgs doublets in the supersymmetric standard model, one has either a small $Lambda$ or a big enough SUSY-breaking scale, but not both. The introduction of the Higgs fields (with their soft terms) allows a small $Lambda$ and a big enough SUSY-breaking scale simultaneously. Since an exponentially small $Lambda$ is statistically preferred (as the properly normalized probability distribution $P(Lambda)$ diverges at $Lambda=0^{+}$), identifying the observed $Lambda_{rm obs}$ to the median value $Lambda_{50%}$ yields $m_{rm EW} sim 100$ GeV. We also find that the warped anti-D3-brane tension has a SUSY-breaking scale of $100m_{rm EW}$ in the landscape while the SUSY-breaking scale that directly correlates with the Higgs fields in the visible sector has a value of $m_{rm EW}$.
Guided by the naturalness criterion for an exponentially small cosmological constant, we present a string theory motivated 4-dimensional $mathcal{N}=1$ non-linear supergravity model (or its linear version with a nilpotent superfield) with spontaneous supersymmetry breaking. The model encompasses the minimal supersymmetric standard model, the racetrack Kahler uplift, and the KKLT anti-$rm D3$-branes, and use the nilpotent superfield to project out the undesirable interaction terms as well as the unwanted degrees of freedom to end up with the standard model (not the supersymmetric version) of strong and electroweak interactions.
The cosmology of branes undergoing the self-tuning mechanism of the cosmological constant is considered. The equations and matching conditions are derived in several coordinate systems, and an exploration of possible solution strategies is performed. The ensuing equations are solved analytically in the probe brane limit. We classify the distinct behavior for the brane cosmology and we correlate them with properties of the bulk (static) solutions. Their matching to the actual universe cosmology is addressed.
Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of an NP-hard problem. The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order $10^{-120}$ in a randomly generated $10^9$-dimensional ADK landscape.
We study the symmetry breaking phenomenon in the standard model during the electroweak phase transition in the presence of a constant hypermagnetic field. We compute the finite temperature effective potential up to the contribution of ring diagrams in the weak field, high temperature limit and show that under these conditions, the phase transition becomes stronger first order.
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