Quantum Gravity as Sum over Spacetimes

Asymptotic Safety, Fractals, and Cosmology

“…The result is a family of RG trajectories where the classical regime becomes more and more pronounced. Subsequently, these solutions are substituted into (65) and (66), which give D s (t; g init , λ init ) and D w (t; g init , λ init ) in dependence of the RG-time t ≡ ln(k) and the RG trajectory. One can verify explicitly, that substituting the RG trajectory into the return probability (49) and computing the spectral dimension from (34) by carrying out the resulting integrals numerically gives rise to the same picture.…”

“…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.…”

The transfer matrix in four-dimensional CDT

“…The CDT transfer matrix has a similar property [3][4][5]. 1 In this article we will analyze an "effective" transfer matrix of CDT to be defined below.…”

“…Under these assumptions the dynamical variable is the scale factor a(t) of the universe and the quantum field theory of the universe is reduced to quantum mechanics of a single variable a(t). The 4D Causal Dynamical Triangulation model (CDT) of quantum gravity is by construction a (regularized) quantum field theory model which is compatible with spatial homogeneity and isotropy (for reviews see [1][2][3]). It uses the path integral formulation and assumes there exists a foliation in (proper) time.…”

Quantum Gravity via Causal Dynamical Triangulations

“…For a more detailed description of the CDT construction we refer the interested reader to [22,23,24].…”