Warping with dilatation symmetry and self-tuning of the cosmological
  constant
  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 $\Gamma$ in
dimension $d>4$ to an effective four-dimensional theory of gravity with a
dilaton field. We find a stable flat phase in the space of extrema of $\Gamma$
which results in a vanishing four-dimensional cosmological constant $\Lambda$.
In order to understand the self-tuning mechanism leading to $\Lambda = 0$ we
discuss in detail the most general warped geometries with maximal
four-dimensional symmetry and $SO(d-4)$ isometry of internal space. While the
solutions of the $d$-dimensional field equations admit singular spaces with
arbitrary $\Lambda$, the extremum condition for $\Gamma$ imposes additional
restrictions which result in $\Lambda = 0$. In cosmology, the dilatation
symmetric fixed point may only be reached for asymptotic time $t \to \infty$.
At finite $t$ dilatation anomalies result in an effective potential and mass
for the pseudo-dilaton or cosmon and in dark energy.
