Quantum gravity on foliated spacetimes: Asymptotically safe and sound

Abstract

Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the non-Gaussian fixed points characteristic for Asymptotic Safety the setting exhibits a second family of non-Gaussian fixed points with a positive Newton's constant and real critical exponents. The presence of these new fixed points alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the -expansion around two dimensions, Monte Carlo simulations based on Lattice Quantum Gravity, and the discretized Wheeler-deWitt equation.

Black hole shadow of a rotating scale-dependent black hole

“…A surprising feature of the above solution is the behavior for a very large and very small radius. This asymptotic behavior reflects the gravitational instability predicted and found in certain AS scenarios [137,[151][152][153] and not the k ∼ 1/r relation one would obtain from a naive dimensional guess.…”

Quantum Spacetime and the Renormalization Group: Progress and Visions

“…These were obtained in a relatively simple truncation for the effective average action meaning that such numbers come with systematic errors and a check of apparent convergence of the results is definitely needed. Nevertheless, these numbers are compatible with those obtained for the critical exponents associated to the fixed point obtained in the asymptotic safety program in three dimensions [64]. It is definitely too early to state that such fixed points belong to the same universality class and that tensor models and asymptotic safety could be completely different point of views of the same physics.…”

Background independent quantum field theory and gravitating vacuum fluctuations

“…It will be an interesting challenge for the future research to confirm this "multi-fractal" character of spacetime [45][46][47][48] by explicit calculations that do not rely on the effective field theory interpretation [49]. 19 It would also be interesting to study the extension of the present work to include the RG flow of non-metric theories of various types [51][52][53][54][55][56][57][58][59].…”