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arXiv · hep-th/0610281

Ricci flows and expansion in axion-dilaton cosmology

Ioannis Bakas·Domenico Orlando·P. Marios Petropoulos
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Abstract

We study renormalization-group flows by deforming a class of conformal sigma-models. We consider overall scale factor perturbation of Einstein spaces as well as more general anisotropic deformations of three-spheres. At leading order in alpha, renormalization-group equations turn out to be Ricci flows. In the three-sphere background, the latter is the Halphen system, which is exactly solvable in terms of modular forms. We also analyze time-dependent deformations of these systems supplemented with an extra time coordinate and time-dependent dilaton. In some regimes time evolution is identified with renormalization-group flow and time coordinate can appear as Liouville field. The resulting space-time interpretation is that of a homogeneous isotropic Friedmann-Robertson-Walker universe in axion-dilaton cosmology. We find as general behaviour the superposition of a big-bang (polynomial) expansion with a finite number of oscillations at early times. Any initial anisotropy disappears during the evolution.

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Ioannis Bakas, Domenico Orlando, P. Marios Petropoulos. 2008-02-06. Ricci flows and expansion in axion-dilaton cosmology. https://doi.org/10.1088/1126-6708%2F2007%2F01%2F040

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