| Summary: | We study the detailed evolution of the fine-structure constant α in the string-inspired runaway dilaton class of models of Damour, Piazza and Veneziano. We provide constraints on this scenario using the most recent α measurements and discuss ways to distinguish it from alternative models for varying α. For model parameters which saturate bounds from current observations, the redshift drift signal can differ considerably from that of the canonical ΛCDM paradigm at high redshifts. Measurements of this signal by the forthcoming European Extremely Large Telescope (E-ELT), together with more sensitive α measurements, will thus dramatically constrain these scenarios. Keywords: Cosmology, Dynamical dark energy, Fine-structure constant, Astrophysical observations
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