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Register a new userLinking Light Scalar Modes with A Small Positive Cosmological Constant in String Theory
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Based on the studies in Type IIB string theory phenomenology, we conjecture that a good fraction of the meta-stable de Sitter vacua in the cosmic stringy landscape tend to have a very small cosmological constant $Lambda$ when compared to either the string scale $M_S$ or the Planck scale $M_P$, i.e., $Lambda ll M_S^4 ll M_P^4$. These low lying de Sitter vacua tend to be accompanied by very light scalar bosons/axions. Here we illustrate this phenomenon with the bosonic mass spectra in a set of Type IIB string theory flux compactification models. We conjecture that small $Lambda$ with light bosons is generic among de Sitter solutions in string theory; that is, the smallness of $Lambda$ and the existence of very light bosons (may be even the Higgs boson) are results of the statistical preference for such vacua in the landscape. We also discuss a scalar field $phi^3/phi^4$ model to illustrate how this statistical preference for a small $Lambda$ remains when quantum loop corrections are included, thus bypassing the radiative instability problem.
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With no free parameter (except the string scale $M_S$), dynamical flux compactification in Type IIB string theory determines both the cosmological constant (vacuum energy density) $Lambda$ and the Planck mass $M_P$ in terms of $M_S$, thus yielding their relation. Following elementary probability theory, we find that a good fraction of the meta-stable de Sitter vacua in the cosmic string theory landscape tend to have an exponentially small cosmological constant $Lambda$ compared to either the string scale $M_S$ or the Planck scale $M_P$, i.e., $Lambda ll M_S^4 ll M_P^4$. Here we illustrate the basic stringy ideas with a simple scalar field $phi^3$ (or $phi^4$) model coupled with fluxes to show how this may happen and how the usual radiative instability problem is bypassed (since there are no parameters to be fine-tuned). These low lying semi-classical de Sitter vacua tend to be accompanied by light scalar bosons/axions, so the Higgs boson mass hierarchy problem may be ameliorated as well.
We construct supersymmetric $mathrm{AdS}_4$ vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the $alpha$ expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude $ < 10^{-123}$ in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.
We study the probability distribution P(Lambda) of the cosmological constant Lambda in a specific set of KKLT type models of supersymmetric IIB vacua. We show that, as we sweep through the quantized flux values in this flux compactification, P(Lambda) behaves divergent at Lambda =0^- and the median magnitude of Lambda drops exponentially as the number of complex structure moduli h^{2,1} increases. Also, owing to the hierarchical and approximate no-scale structure, the probability of having a positive Hessian (mass squared matrix) approaches unity as h^{2,1} increases.
We investigate the decay of metastable de Sitter, Minkowski and anti-de Sitter vacua catalyzed by a black hole and a cloud of strings. We apply the method to the creation of the four dimensional bubble universe in the five dimensional anti-de Sitter spacetime recently proposed by Banerjee, Danielsson, Dibitetto, Giri and Schillo. We study the bounce action for the creation and find that the bubble with very small cosmological constant, of order $Lambda^{(4)}/M^2_4 sim 10^{-120}$, is favored by the catalysis by assuming appropriate mass scales of the black hole and the cloud of strings to reproduce the present energy densities of matter and radiation in the bubble universe.
We apply Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers in the context of finding chiral heterotic string models with positive cosmological constant from $mathbb{Z}_2times mathbb{Z}_2$ orbifolds. The power of using SAT/SMT solvers to sift large parameter spaces quickly to decide satisfiability, both to declare and prove unsatisfiability and to declare satisfiability, are demonstrated in this setting. These models are partly chosen to be small enough to plot the performance against exhaustive search, which takes around 2 hours 20 minutes to comb through the parameter space. We show that making use of SMT based techniques with integer encoding is rather simple and effective, while a more careful Boolean SAT encoding provides a significant speed-up -- determining satisfiability or unsatisfiability has, in our experiments varied between 0.03 and 0.06 seconds, while determining all models (where models exist) took 19 seconds for a constraint system that allows for 2048 models and 8.4 seconds for a constraint system that admits 640 models. We thus gain several orders of magnitude in speed, and this advantage is set to grow with a growing parameter space. This holds the promise that the method scales well beyond the initial problem we have used it for in this paper.
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