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 nonGaussian 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 ArnowittDeserMisner formalism for evaluating the gravitational renormalization group flow on a cosmological FriedmannRobertsonWalker background. Besides possessing the nonGaussian fixedpoint characteristic for asymptotic safety the setting exhibits a second family of nonGaussian 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 ɛ expansion around two dimensions, Monte Carlo simulations based on lattice quantum gravity, and the discretized WheelerDeWitt equation.
 Publication:

Physical Review D
 Pub Date:
 April 2017
 DOI:
 10.1103/PhysRevD.95.086013
 arXiv:
 arXiv:1609.04813
 Bibcode:
 2017PhRvD..95h6013B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 7 pages, 3 figures. Conclusions slightly modified