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Register a new userFast optimization algorithms and the cosmological constant
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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.
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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.
We present a non-supersymmetric theory with a naturally light dilaton. It is based on a 5D holographic description of a conformal theory perturbed by a close-to-marginal operator of dimension 4-epsilon, which develops a condensate. As long as the dimension of the perturbing operator remains very close to marginal (even for large couplings) a stable minimum at hierarchically small scales is achieved, where the dilaton mass squared is suppressed by epsilon. At the same time the cosmological constant in this sector is also suppressed by epsilon, and thus parametrically smaller than in a broken SUSY theory. As a byproduct we also present an exact solution to the scalar-gravity system that can be interpreted as a new holographic realization of spontaneously broken conformal symmetry. Even though this metric deviates substantially from AdS space in the deep IR it still describes a non-linearly realized exactly conformal theory. We also display the effective potential for the dilaton for arbitrary holographic backgrounds.
We construct a vacuum of string theory in which the magnitude of the vacuum energy is $< 10^{-123}$ in Planck units. Regrettably, the sign of the vacuum energy is negative, and some supersymmetry remains unbroken.
The today estimated value of dark energy can be achieved by the vacuum condensate induced by neutrino mixing phenomenon. Such a tiny value is recovered for a cut-off of the order of Planck scale and it is linked to the sub eV neutrino mass scale. Contributions to dark energy from auxiliary fields or mechanisms are not necessary in this approach.
There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterize different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models. This essay was submitted to the Gravity Research Foundation Competition and is based on a longer article, which will be submitted in the near future.
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