Emergence of a 4D World from Causal Quantum Gravity

Abstract

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic four-dimensional world emerges from this theory dynamically.

A functional renormalization group equation for foliated spacetimes

“…The direction singled out by the S 1 allows to Wickrotate between Euclidean and Lorentzian signature, and will thus be referred to as (Euclidean) time direction. Notably, the ADM construction is very close to the geometric setting underlying the Monte-Carlo simulations of Causal Dynamical Triangulations (CDT) [27,28,29,30,31].…”

Asymptotic Safety, Fractals, and Cosmology

“…Along a different line of investigations, the Causal Dynamical Triangulation (CDT) approach has been developed and first Monte-Carlo simulations were performed [59][60][61][62][63][64], see [65] for a recent review. In this framework one attempts to compute quantum gravity partition functions by numerically constructing the continuum limit of an appropriate statistical mechanics system.…”

Astrophysical implications of the Asymptotic Safety Scenario in Quantum Gravity

“…In particular it has been shown [6,22] that these spacetimes have fractal properties, with a fractal dimension of 2 at small, and 4 at large distances. The same dynamical dimensional reduction was also observed in numerical studies of Lorentzian dynamical triangulations [25][26][27] and in [28] A.Connes et al speculated about its possible relevance to the non-commutative geometry of the standard model.…”