The cosmological constant and higher dimensional dilatation symmetry

TL;DR

This paper explores how higher-dimensional dilatation symmetry and fixed points in quantum gravity can lead to a vanishing cosmological constant, providing a potential explanation for dark energy and its small observed value.

Contribution

It proposes a fixed point scenario with no scalar potential that results in a vanishing four-dimensional cosmological constant through dimensional reduction.

Findings

Stable solutions with zero effective four-dimensional constant.

Cosmological solutions approaching the fixed point lead to asymptotically vanishing dark energy.

Explicit higher-dimensional geometries realizing these solutions are discussed.

Abstract

We discuss the hypothesis of a fixed point for quantum gravity coupled to a scalar, in the limit where the scalar field goes to infinity, accompanied by a suitable scaling of the metric. We propose that no scalar potential is present for the dilatation symmetric quantum effective action at the fixed point. Dimensional reduction of such a higher dimensional effective action leads to solutions with a vanishing effective four-dimensional constant. Under rather general circumstances these are the only quasistatic stable solutions with finite four-dimensional gravitational constant. If cosmological runaway solutions approach the fixed point as time goes to infinity, the cosmological constant vanishes asymptotically. For our old Universe the fixed point is not yet reached completely, resulting in a tiny amount of dark energy, comparable to dark matter. We discuss explicitly higher dimensional geometries which realize such asymptotic solutions for $t\to\infty$. They include Ricci-flat spaces as well as warped spaces, potentially with singularities.