Warping with dilatation symmetry and self-tuning of the cosmological constant

TL;DR

This paper explores how an ultraviolet fixed point in quantum gravity can lead to a natural self-tuning mechanism that results in a vanishing cosmological constant through dimensional reduction and stable extrema of an effective action.

Contribution

It demonstrates a self-tuning mechanism in quantum gravity with dilatation symmetry that enforces a zero cosmological constant in the effective four-dimensional theory.

Findings

Stable flat phase with zero cosmological constant identified.

Extremum conditions restrict solutions to achieve $ extLambda=0$.

Dilatation anomalies at finite time generate dark energy.

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 $\Gamma$ 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.