Asymptotic safety of quantum gravity beyond Ricci scalars

TL;DR

This paper explores the asymptotic safety of quantum gravity by including curvature invariants beyond Ricci scalars, analyzing fixed points and their implications for cosmology and inflation.

Contribution

It extends the asymptotic safety analysis to include Ricci tensor invariants, providing new insights into fixed points and their stability in quantum gravity.

Findings

Ricci tensor invariants stabilize the UV fixed point.

Higher-dimensional couplings show near-Gaussian scaling.

The fixed point admits inflationary solutions.

Abstract

We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalisation with high order polynomial approximations and full numerical integration we derive the renormalisation group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterised by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilise the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from $f(R)$-type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.