Asymptotic safety in the f(R) approximation

TL;DR

This paper investigates the existence and properties of fixed points in the asymptotic safety approach to quantum gravity using f(R) approximations, revealing lines of fixed points and the importance of topology change.

Contribution

It demonstrates that the latest f(R) approximation admits lines of fixed points and analyzes their properties, advancing understanding beyond polynomial truncations.

Findings

Earlier versions lack smooth fixed point solutions due to singularities.

The most recent version features lines of fixed points with continuous eigen-perturbation spectra.

Incorporating topology change may lead to sensible fixed point behavior.

Abstract

In the asymptotic safety programme for quantum gravity, it is important to go beyond polynomial truncations. Three such approximations have been derived where the restriction is only to a general function f(R) of the curvature R>0. We confront these with the requirement that a fixed point solution be smooth and exist for all non-negative R. Singularities induced by cutoff choices force the earlier versions to have no such solutions. However, we show that the most recent version has a number of lines of fixed points, each supporting a continuous spectrum of eigen-perturbations. We uncover and analyse the first five such lines. Sensible fixed point behaviour may be achieved if one consistently incorporates geometry/topology change. As an exploratory example, we analyse the equations analytically continued to R<0, however we now find only partial solutions.We show how these results are always consistent with, and to some extent can be predicted from, a straightforward analysis of the constraints inherent in the equations.