De Sitter quantum gravity within the covariant Lorentzian approach to asymptotic safety

TL;DR

The paper tackles the problem of obtaining a UV-complete, Lorentzian quantum gravity theory in a de Sitter background by applying a covariant functional renormalization group approach to the Einstein–Hilbert truncation. It develops a Lorentzian FRGE with a local, mass-like regulator and Hadamard renormalization, computes the Hadamard-consistent propagators for massive scalars, vectors, and tensors in de Sitter space, and uses these to derive the flow of the running Newton and cosmological constants. The main result is the explicit evidence for a non-trivial UV fixed point across common gauges, with the fixed-point values and critical exponents showing gauge- and Hadamard-scale dependence but qualitatively matching Euclidean results, thereby supporting the asymptotic safety scenario in a Lorentzian setting. The work lays the groundwork for gauge-invariant observables, higher-truncation analyses, and comparisons with cosmological correlators and CDT, and it highlights the role of state dependence and the Hadamard scale in shaping the RG flow.

Abstract

Recent technical and conceptual advancements in the asymptotic safety approach to quantum gravity have enabled studies of the UV completion of Lorentzian Einstein gravity, emphasizing the role of the state dependence. We present here the first complete investigation of the flow equations of the Einstein-Hilbert action within a cosmological spacetime, namely de Sitter spacetime. Using the newly derived graviton propagator for general gauges and masses in de Sitter spacetime, we analyze the dependence on the gauge and on finite renormalization parameters. Our results provide evidence of a UV fixed point for the most commonly used gauges.

Figures (17)

• Figure 1: Flow diagram with $\zeta = \frac{1}{2}$ and $\xi = 1$ for different values of $\alpha$.
• Figure 2: UV fixed points with $\zeta = \frac{1}{2}$ and $\xi = 1$ for different values of $\alpha$.
• Figure 3: Critical exponents with $\zeta = \frac{1}{2}$ and $\xi = 1$ for different values of $\alpha$.
• Figure 4: Flow diagram with $\zeta = \frac{1}{2}$ and $\alpha = \frac{2}{5}$, for different values of $\xi$.
• Figure 5: UV fixed point with $\zeta = \frac{1}{2}$ and $\alpha = \frac{2}{5}$ for different values of $\xi$.