Scaling solutions for Dilaton Quantum Gravity

TL;DR

This paper explores scaling solutions in dilaton quantum gravity using the functional renormalization group, revealing fixed points, spontaneous scale symmetry breaking, and implications for cosmology including natural inflation and a dynamical cosmological constant.

Contribution

It introduces numerical scaling solutions connecting UV and IR fixed points in dilaton quantum gravity, with applications to cosmology and spontaneous scale symmetry breaking.

Findings

Identification of numerical solutions connecting UV and IR fixed points

Spontaneous breaking of scale symmetry with a non-zero scalar field value

Emergence of natural inflation and a vanishing effective cosmological constant

Abstract

Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale $k$ is varied. In the Einstein frame the quantum effective action corresponding to the scaling solutions becomes independent of $k$. The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity.