We found double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F = S T U .The area formula is S T U -moduli independent and has [SL (2; Z)] 3 symmetry in space of charges. The dual version of this theory without prepotential treats the dilaton S asymmetric versus T ; U -moduli. We display the dual relation between new (STU) black holes and stringy (SjT U ) black holes using particular S p (8; Z) transformation. The area formula of one theory equals the area formula of the dual theory when expressed in terms of dual charges.We analyse the relation between (STU)black holes to string triality of black holes: (SjT U ), (T jU S ), (UjST) solutions. In democratic S T U -symmetric version we nd that all three S and T and U duality symmetries are non-perturbative and mix electric and magnetic charges.
We propose a description of dark energy and acceleration of the universe in extended supergravities with de Sitter (dS) solutions. Some of them are related to M-theory with non-compact internal spaces. Masses of ultra-light scalars in these models are quantized in units of the Hubble constant: m 2 = n H 2 . If dS solution corresponds to a minimum of the effective potential, the universe eventually becomes dS space. If dS solution corresponds to a maximum or a saddle point, which is the case in all known models based on N = 8 supergravity, the flat universe eventually stops accelerating and collapses to a singularity. We show that in these models, as well as in the simplest models of dark energy based on N = 1 supergravity, the typical time remaining before the global collapse is comparable to the present age of the universe, t = O(10 10 ) years. We discuss the possibility of distinguishing between various models and finding our destiny using cosmological observations.
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