Abstract
We investigate consequences of an ultraviolet fixed point in quantum gravity for the cosmological constant. For this purpose we perform dimensional reduction of a general dilatation-symmetric effective action in dimension to an effective four-dimensional theory of gravity with a dilaton field. We find a stable flat phase in the space of the extrema of which results in a vanishing four-dimensional cosmological constant . In order to understand the self-tuning mechanism leading to we discuss in detail the most general warped geometries with maximal four-dimensional symmetry and isometry of internal space. While the solutions of the -dimensional field equations admit singular spaces with arbitrary , the extremum condition for imposes additional restrictions which result in . In cosmology, the dilatation-symmetric fixed point may only be reached for asymptotic time . At finite dilatation anomalies result in an effective potential and mass for the pseudodilaton or cosmon and in dark energy.
- Received 22 March 2010
DOI:https://doi.org/10.1103/PhysRevD.81.103508
©2010 American Physical Society