How round is the quantum de Sitter universe?

Abstract

We investigate the quantum Ricci curvature, which was introduced in earlier work, in full, four-dimensional quantum gravity, formulated nonperturbatively in terms of Causal Dynamical Triangulations (CDT). A key finding of the CDT approach is the emergence of a universe of de Sitter-type, as evidenced by the successful matching of Monte Carlo measurements of the quantum dynamics of the global scale factor with a semiclassical minisuperspace model. An important question is whether the quantum universe exhibits semiclassicality also with regard to its more local geometric properties. Using the new quantum curvature observable, we examine whether the (quasi-)local properties of the quantum geometry resemble those of a constantly curved space. We find evidence that on sufficiently large scales the curvature behaviour is compatible with that of a four-sphere, thus strengthening the interpretation of the dynamically generated quantum universe in terms of a de Sitter space.

New topological observables in a model of Causal Dynamical Triangulations on a torus

“…As seems to follow from [85], the results for a 4D spherical configuration regardless of the choice of simplex at which the average sphere distance is measured correspond to the outgrowth simplices in the toroidal case. It suggests that a 4D spherical configuration can be visualized as built out only of outgrowths, with no classical part.…”

“…Because the spatial structure of a toroidal CDT is better understood and, moreover, apparently richer than that of spherical CDT, it is of interest to check if analyzing quantum Ricci curvature can add something to this understanding or at least confirm the previous discoveries, and if the results differ from those reported in [85] for the case of spherical spatial topology.…”

“…The quantum Ricci curvature was introduced by Klitgaard and Loll in [83]. It was calculated by the same authors for smooth model spaces and regular lattices in the same paper, and then tested on 2D DT in [84] and on 4D CDT with spherical spatial topology in [85]. This section will summarize the motivation and the definitions; a complete discussion of the results is contained in the articles cited.…”

“…(5.1) was in [83] calculated and plotted as a function of δ for smooth hyperbolic, flat and spherical model spaces, regular square, hexagonal and honeycomb lattices, and for so-called Delauney triangulations of a plane. In the next article, [84], the same was performed for two-dimensional DT, and, finally, in the third article of the same authors, [85], the quantity was plotted for configurations in the C phase of four-dimensional CDT with the spatial topology of a 3-sphere.…”

Compact gauge fields on Causal Dynamical Triangulations: a 2D case study

“…A standard discretization is the one based on the Regge formalism [2], where space-time configurations are represented by triangulations, i.e., collections of flat simplexes glued together according to different geometries. Promising results have been obtained, in particular, by exploring Causal Dynamical Triangulations (CDT) [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], where one enforces an additional condition of global hyperbolicity by means of a space-time foliation [19].…”