10. January 2024

Generalized Causal Dynamical Triangulations

Figure This simulation show a generalized CDT geometry with a large number of topology changes. The colors indicate equal-time bands.

Figure This is a causal triangulation with no topology change, sampled from the regular CDT partition function.

Figure A triangulation with several topology changes sampled from the generalized CDT partition function.

Figure This triangulation shows a higher abundance of topology changes.

Video A compilation of several typical geometries sampled from the generalized CDT partition function. Here boundary conditions are used in which the size of the spatial universe at final time is fixed. By varying this size as well as the time extent and weight for the topology changes one obtains a rather diverse collection of geometries.

References

[1] Ambjørn, Jan, Renate Loll, Willem Westra, and Stefan Zohren. Putting a cap on causality violations in causal dynamical triangulations. Journal of High Energy Physics 2007, no. 12 (2007): 017.

[2] Ambjørn, Jan, and Timothy Budd. Trees and spatial topology change in causal dynamical triangulations. Journal of Physics A: Mathematical and Theoretical 46, no. 31 (2013): 315201.