The cosmological constant and higher dimensional dilatation symmetry

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.

Extension of argument why higher dimensional dilatation symmetry leads to asymptotic self-tuning of cosmological constant to zero. Part of material of first version has been moved to arXiv:1003.3809 because of length of paper. 21 pages, 1 figure

References in corpus (9)

• Cosmology and the Fate of Dilatation Symmetry
• Quantum scale invariance, cosmological constant and hierarchy problem
• Scale invariance, unimodular gravity and dark energy
• Growing Matter
• Growing neutrinos and cosmological selection
• Naturalness of exponential cosmon potentials and the cosmological constant problem
• Dilatation symmetry in higher dimensions and the vanishing of the cosmological constant
• Warping with dilatation symmetry and self-tuning of the cosmological constant
• Constraints for warped branes

Cited by in corpus (10)

• Dark Energy
• Inflation, quintessence, and the origin of mass
• Weyl transverse gravity (WTDiff) and the cosmological constant
• Modified gravity and coupled quintessence
• Coupled dark energy and dark matter from dilatation anomaly
• Small scale structures in coupled scalar field dark matter
• Warping with dilatation symmetry and self-tuning of the cosmological constant
• Chameleonic dilaton and conformal transformations
• Species, chameleonic strings and the concept of particle
• Sign Switching Dark Energy from a Running Barrow Entropy