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Register a new userThe Cosmological Constant and the Electroweak Scale
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String theory has no parameter except the string scale, so a dynamically compactified solution to 4 dimensional spacetime should determine both the Planck scale and the cosmological constant $Lambda$. In the racetrack Kahler uplift flux compactification model in Type IIB theory, where the string theory landscape is generated by scanning over discrete values of all the flux parameters, a statistical preference for an exponentially small $Lambda$ is found to be natural (arXiv:1305.0753). Within this framework and matching the median $Lambda$ value to the observed $Lambda$, a mass scale ${bf m}simeq 100$ GeV naturally appears. We explain how the electroweak scale can be identified with this mass scale.
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It is well known that anthropic selection from a landscape with a flat prior distribution of cosmological constant Lambda gives a reasonable fit to observation. However, a realistic model of the multiverse has a physical volume that diverges with time, and the predicted distribution of Lambda depends on how the spacetime volume is regulated. We study a simple model of the multiverse with probabilities regulated by a scale-factor cutoff, and calculate the resulting distribution, considering both positive and negative values of Lambda. The results are in good agreement with observation. In particular, the scale-factor cutoff strongly suppresses the probability for values of Lambda that are more than about ten times the observed value. We also discuss several qualitative features of the scale-factor cutoff, including aspects of the distributions of the curvature parameter Omega and the primordial density contrast Q.
We introduce a novel method to circumvent Weinbergs no-go theorem for self-tuning the cosmological vacuum energy: a Lorentz-violating finite-temperature superfluid can counter the effects of an arbitrarily large cosmological constant. Fluctuations of the superfluid result in the graviton acquiring a Lorentz-violating mass and we identify a unique class of theories that are pathology free, phenomenologically viable, and do not suffer from instantaneous modes. This new and hitherto unidentified phase of massive gravity propagates the same degrees of freedom as general relativity with an additional Lorentz-violating scalar that is introduced by higher-derivative operators in a UV insensitive manner. The superfluid is therefore a consistent infrared modification of gravity. We demonstrate how the superfluid can degravitate a cosmological constant and discuss its phenomenology.
We suggest a solution to the problem of some apparently excessive contributions to the cosmological constant from Standard-Model condensates.
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.
A scenario based on the scale invariance for explaining the vanishing cosmological constant (CC) is discussed. I begin with a notice on the miraculous fact of the CC problem that the vacuum energies totally vanish at each step of hierarchical and successive spontaneous symmetry breakings. I then argue that the classical scale invariance is a necessary condition for the calculability of the vacuum energy. Next, I discuss how sufficient the scale invariance is for solving the CC problem. First in the framework of classical field theory, the scale invariance is shown to give a natural mechanism for realizing the miracle of vanishing vacuum energies at every step of spontaneous symmetry breakings. Then adopting Englert-Truffin-Gastmans prescription to maintain the scale invariance in quantum field theory, I point out that the quantum scale invariance alone is not yet sufficient to avoid the superfine tuning of coupling constants for realizing vanishingly small cosmological constant, whereas the hierarchy problem may be solved. Another symmetry or a mechanism is still necessary which protects the flat direction of the potential against the radiative corrections.
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