Quantum gravity and scale symmetry in cosmology

C. Wetterich

Submitted on 7 November 2022


We discuss predictions for cosmology which result from the scaling solution of functional flow equations for a quantum field theory of gravity. A scaling solution is necessary to render quantum gravity renormalizable. Our scaling solution is directly connected to the quantum effective action for the metric coupled to a scalar field. It includes all effects of quantum fluctuations and is invariant under general coordinate transformations. Solving the cosmological field equations derived by variation of the quantum effective action provides for a detailed quantitative description of the evolution of the universe. The \qq{beginning state} of the universe is found close to an ultraviolet fixed point of the flow equation. It can be described by an inflationary epoch, with approximate scale invariance of the observed primordial fluctuation spectrum explained by approximate quantum scale symmetry. Overall cosmology realizes a dynamical crossover from the ultraviolet fixed point to an infrared fixed point which is approached in the infinite future. Present cosmology is close to the infrared fixed point. It features dynamical dark energy mediated by a light scalar field. The tiny mass of this cosmon arises from its role as a pseudo Goldstone boson of spontaneously broken quantum scale symmetry. The extremely small value of the present dark energy density in Planck units results dynamically as a consequence of the huge age of the universe. The cosmological constant problem finds a dynamical solution. We present a detailed quantitative computation of the scaling solution for the scalar effective potential and the field-dependent coefficient of the curvature scalar. This allows for further quantitative predictions.


Comment: 31 pages, 2 figures

Subjects: General Relativity and Quantum Cosmology; Astrophysics - Cosmology and Nongalactic Astrophysics; High Energy Physics - Theory


\emph{Effective scalar potential}. We plot $\Vhat$, the potential in the Einstein frame in Planck units, as a function of the scalar field $x=\ln\rhotil=\vp/(2M)$. One observes the typical flat tail for negative and small $x$, and the exponential decrease for large $x$.