Reconstructing the Universe

Abstract

We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time.Comment: 52 pages, 20 postscript figures, added reference

On a renormalization group scheme for causal dynamical triangulations

“…The particular quantum theory of gravity defined by the partition function (2.5) for the action (2.8) exhibits three phases of quantum geometry: the decoupled phase A, the crumpled phase B, and the physical phase C [14,31]. The A-C phase transition is of first order, the B-C phase transition is of second order, and the order of the A-B phase transition has not been ascertained [8,9].…”

The transfer matrix in four-dimensional CDT

“…The set of Euclidean geometries we obtain in this way is a subset of the DT Euclidean geometries and this restriction seemingly cures some of the higher dimensional DT diseases, while in two dimensions the relation between the restricted theory and the full DT theory has been worked out in detail: one obtains the CDT theory from the DT theory by integrating out all baby universes (which results in a non-analytic mapping between the coupling constants of the two theories), and (somewhat surprisingly) one can restore the DT theory from the CDT theory by the inverse mapping [45,46]. Using four-simplices (which is the case having our attention in this article) as building blocks one can, for suitable choices of bare coupling constants, observe a four-dimensional (Euclidean) universe [47,48]. For these choices of coupling constants the shape of the universe is consistent with an interpretation as an (Euclidean) de Sitter space, at least as long as one looks at the scale factor [49,50].…”

Signature change of the metric in CDT quantum gravity?

“…There are two types of fundamental building blocks in CDT, the (4, 1) and (3, 2) simplices (see ref. [12] for a detailed discussion of the numerical setup), the number of which are quantified by N 4,1 and N 3,2 , respectively. N 0 is the number of vertices in the triangulation T .…”

“…Evidence for such a fixed point has come mainly from functional renormalization group methods [6][7][8][9][10][11] and lattice approaches to quantum gravity [12][13][14][15]. In a lattice formulation of quantum gravity a non-trivial fixed point would appear as a second-order critical point, the approach to which would define a continuum limit [16].…”